The Polynesian game is for players who like clicking "End Turn" over and over again.
Okay, that's not entirely fair, but their UHV game is one you can play while watching videos on another screen, or while reading a book.
UHV Conditions
1. By Turn 200, establish settlements on two of the following island groups: Hawaii, the Marquesas, New Zealand, Easter Island.
2. By Turn 220, establish settlements on all four of the above island groups.
3. By Turn 240, build the Moai Statues.
Given the expense and resources necessary for their construction, the Moai Statues in practice can only be built on Easter Island, so even the third condition is a spread condition like the first two.
The special challenge is that all of these groups are cut off from your starting islands by Ocean and Cape tiles, and the only way to cross these (absent ocean-going vessels, which you are not going to be able to tech in time for the deadline) is by enveloping these tiles with your culture. Then you use Wakas (the Polynesians UU) to enter and cross them.
So you have to build culture. That's what the Polynesian Mana'e is for: it generates culture and also lets you hire an artist to spread your culture faster. With those and the Atua shrines, you can build out culture into the tiles you need to enter to get to your destinations.
So that's the Polynesian game: Build a city on a strategic island. Build a Mana'e; hire an artist; build an Atua shrine. When your culture expands, cross to the next strategic island and repeat. When you reach Easter Island, build a Mana'e to elevate your culture enough that you can build the Moai Wonder.
I could leave the rest as an exercise to the player, but here are some useful notes:
Starting Location
You have four islands at the start. Ignore the Sugar island, as it is Foreign Territory, and build on two of the others. I recommend building on the eastern island—Niue—as one of the two, as you'll need a head start with it on building, as it is relatively resource poor. Built Atua Shrines while you research Ceremony, which you need for the Mana'e; also, build another settler to colonize the third island in the group.
Wakas can be used to carry a single unit, but they can also be sacrificed like Workboats onto sea resources. After settling the third island, you can sacrifice your starting Waka to bring the second sea resource in the archipelago online.
Once you have discovered Ceremony, shift to producing Mana'e and hiring artists; once you've done this on all three of your islands, two islands can shift to producing Settlers, and the third to producing Wakas to carry them.
Once you have spread culture enough that you can leave your starting archipelago (see below), you can fire your artists. Except: Leave one artist in place until you have generated a Great Artist. You will need him.
A Map of the Pacific
Your quest will send you in three directions.
1. South-west from Mua you will find New Zealand, which is one of your destinations.
2. East of Niue you will find another three-island archipelago. Settle the easternmost, Tahiti. North of Tahiti is Nuki Hiva (the Marquesas), which is one of your destinations. East of Tahiti is Mangareva, and east of Mangareva is Rapa Nui (Easter Island), another destination.
3. North of Manu'a is Tokelau; north of Tokelau is Kiritimati; north of Kiritimati is the Hawaiian archipelago, your last destination.
The New Zealand branch is the first corridor likely to open. The second branch is the longest, but each link is relatively easy to cross. The third branch is fairly long, and there are larger gaps between each island. You can therefore delay settling New Zealand until after you've established at least the first steps in the other two branches.
You will have built a Great Artist. You will need to culture bomb one the links in the northern chain (either Tokelau or Kiritimati) in order to cross one of those big gaps in time to reach Hawaii for the deadline.
As noted above, after you have opened a corridor, settle the next island in the sequence; build a Mana'e, hire an artist, build an Atua; switch to Settler production. You will also be building Wakas, which can be placed on food resources (of which there will be several) to speed Settler production and on Pearl resources. Once you have built enough Settlers to populate your destinations, you can switch production to anything else. It won't matter.
Techs, Civics, Garrisons
The tech path is simple: Beeline Ceremony. Beeline Navigation. Beeline Masonry. Then turn off research.
Civics: You can ignore civics until it is time to build the Moai Statues. At that point, institute Deification and Slavery (which you will have discovered).
Garrisons: You don't need them, not even Militias, not even for happiness, in order to win, though you will have to turn off growth.
Okay, that's not entirely fair, but their UHV game is one you can play while watching videos on another screen, or while reading a book.
UHV Conditions
1. By Turn 200, establish settlements on two of the following island groups: Hawaii, the Marquesas, New Zealand, Easter Island.
2. By Turn 220, establish settlements on all four of the above island groups.
3. By Turn 240, build the Moai Statues.
Given the expense and resources necessary for their construction, the Moai Statues in practice can only be built on Easter Island, so even the third condition is a spread condition like the first two.
The special challenge is that all of these groups are cut off from your starting islands by Ocean and Cape tiles, and the only way to cross these (absent ocean-going vessels, which you are not going to be able to tech in time for the deadline) is by enveloping these tiles with your culture. Then you use Wakas (the Polynesians UU) to enter and cross them.
So you have to build culture. That's what the Polynesian Mana'e is for: it generates culture and also lets you hire an artist to spread your culture faster. With those and the Atua shrines, you can build out culture into the tiles you need to enter to get to your destinations.
So that's the Polynesian game: Build a city on a strategic island. Build a Mana'e; hire an artist; build an Atua shrine. When your culture expands, cross to the next strategic island and repeat. When you reach Easter Island, build a Mana'e to elevate your culture enough that you can build the Moai Wonder.
I could leave the rest as an exercise to the player, but here are some useful notes:
Starting Location
You have four islands at the start. Ignore the Sugar island, as it is Foreign Territory, and build on two of the others. I recommend building on the eastern island—Niue—as one of the two, as you'll need a head start with it on building, as it is relatively resource poor. Built Atua Shrines while you research Ceremony, which you need for the Mana'e; also, build another settler to colonize the third island in the group.
Wakas can be used to carry a single unit, but they can also be sacrificed like Workboats onto sea resources. After settling the third island, you can sacrifice your starting Waka to bring the second sea resource in the archipelago online.
Once you have discovered Ceremony, shift to producing Mana'e and hiring artists; once you've done this on all three of your islands, two islands can shift to producing Settlers, and the third to producing Wakas to carry them.
Once you have spread culture enough that you can leave your starting archipelago (see below), you can fire your artists. Except: Leave one artist in place until you have generated a Great Artist. You will need him.
A Map of the Pacific
Your quest will send you in three directions.
1. South-west from Mua you will find New Zealand, which is one of your destinations.
2. East of Niue you will find another three-island archipelago. Settle the easternmost, Tahiti. North of Tahiti is Nuki Hiva (the Marquesas), which is one of your destinations. East of Tahiti is Mangareva, and east of Mangareva is Rapa Nui (Easter Island), another destination.
3. North of Manu'a is Tokelau; north of Tokelau is Kiritimati; north of Kiritimati is the Hawaiian archipelago, your last destination.
The New Zealand branch is the first corridor likely to open. The second branch is the longest, but each link is relatively easy to cross. The third branch is fairly long, and there are larger gaps between each island. You can therefore delay settling New Zealand until after you've established at least the first steps in the other two branches.
You will have built a Great Artist. You will need to culture bomb one the links in the northern chain (either Tokelau or Kiritimati) in order to cross one of those big gaps in time to reach Hawaii for the deadline.
As noted above, after you have opened a corridor, settle the next island in the sequence; build a Mana'e, hire an artist, build an Atua; switch to Settler production. You will also be building Wakas, which can be placed on food resources (of which there will be several) to speed Settler production and on Pearl resources. Once you have built enough Settlers to populate your destinations, you can switch production to anything else. It won't matter.
Techs, Civics, Garrisons
The tech path is simple: Beeline Ceremony. Beeline Navigation. Beeline Masonry. Then turn off research.
Civics: You can ignore civics until it is time to build the Moai Statues. At that point, institute Deification and Slavery (which you will have discovered).
Garrisons: You don't need them, not even Militias, not even for happiness, in order to win, though you will have to turn off growth.
buildings (Pagan Temple and Mala'e) early.
, though its 
is initially poor. Work a Citizen to build the UB early, then an Artist if needed.
resources (3 core cities + Tahiti) need to take turns building Settlers in between 
