I just now watched the video. I am far from the best player but I notice some additional things. Let me know if you disagree with my assessment. I would love the chance to learn. I also couldn't hear the audio.
I don't think a worse settling tile could have been picked. Not a single hill in the whole city. There's simply no way the capital will have enough production to get out of the classical era alive.
Settling to the west between the incense and bananas would have made for a great start and early pantheon. The plains hills to the east also looks like a good spot. Would get the bananas and be within one tile of the diamonds. There's also a plains hills (rainforest) to the north that looks appealing. The plan from the outset should have been to get cities on those three tiles.
At 5:47 the tribal village was ignored! Maybe it wasn't seen. That's a way to make Deity easier. Use a UI mod that makes the tribal villages more noticeable. But so far we are off to a bad start. I can't see the turn count on the video so I'm using time offsets. Another tribal village ignored at 10:09.
At 11:22 you can see the two warriors outside the capital. But no change of plans from building the settler to building a warrior!
Then the builder chop gets used toward the settler. Had the production been switched to warrior, it was a winnable fight. Then at 14:24, more production of a (nearly useless) slinger. There might still have been time to get a warrior build for the garrison strength
If a save file from the turn where the settler was chopped is available, I'd love to try to play it out. I think that I could have, from that point, not only held off the attack, but counter-attacked and taken a city or two off of her hands.
Let me preface this. Deity is hard for me. I apologize if I am over explaining some things or explaining things which are already known to you.
I would have probably moved my warrior atop the stone to hopefully see 2 tiles around it. I would have seen the copper instead of the incense, but the incense is probably a better find. Considering his choice and the visibility of the incense instead, I would probably move between the banana and the stone, and I would expect the incense to be a high priority for the first natural border expansion. I would work the banana right away because I want a pop 2 city quickly, because lately I have been trying to settle my second city as fast as possible. As soon as it went to pop 2, I would switch to the stone and the wooded hills, or incense if/when available, and produce a settler. I would aim to settle near that gold mine for the gold and it is easy to improve to two hammers early in the game.
I like the spot between the banana and gold mine for the second city because they are both in the first ring. Non-capital cities that don't get a free building like Trajan does with the monument, have very little culture and it takes something like 30 turns to grow the border at pop 1. The city does have a banana so it will grow up and expand it little bit faster. Each pop is ~.3 culture, or maybe 1 culture per 3 population. Something like that. I am just going off what he sees at turn 1. Maybe it if viable to settle on the plains hill and get the extra production instead. I like to build warriors/slingers in city 2 and production rules for that. However, a gold per turn gift could be useful too.
Meanwhile, I would have sent my warrior to explore around the gold mine and the other banana, because I am usually interested in finding my second city location asap. Having good food in both cities means I can grow quicker and build up my loyalty pressure of the surrounding territory. Of course, we know that he has a close neighbor to the north, so it is going to cause friction. The rival will have more trouble settling in his direction. Does that tempt the AI to explore his region? I hope so because that would be logical AI, but I don't know. Either way, we know he needs a security force soon, but I tend to want two cities early. If I have a close neighbor, I will often fall into trouble and I have many very close games because of that and I lose a fair percentage of the openings because of the aggressive expansion.
The problem with working the banana is that I would have started a scout while waiting to grow, but I would be highly tempted to suspend building the scout to produce the settler quicker. I often get into trouble when I have a 3/1 tile because delaying the scout increases the likelihood of a dark age and the scout can be useful for slowing down enemy units. I try to get in their way as much as possible. Then it is tempting to look a little bit further with the one warrior but getting too far away is easily punished if the enemy finds you.
I think it a good idea to uncover a 10-hex distance around the capital. Enemy cities within about that range mean an AI with normal movement speed might attack. A scout definitely helps with that, so it might just be better to produce the scout a fast a possible and then afterwards produce the settler as fast as possible. I am still figuring that out and only as a general rule of thumb. Whatever the world map looks like could influence those decisions.
I would consider all civilizations to be bloodthirsty enemies as the game opens on the deity difficulty unless you can get a friendship agreement. Sometimes a gift can help. I have experimented a little with gifts and they can work, but the little that you have often won't be impactful enough if you are discovered very early. However, considering gifts, settling the capital near the gold mine and getting the 3 extra gold per turn could also be a viable strategy if you want an early friend and are willing to delay expansion. You could gift the 3 gold per turn and the AI will value it pretty well, I think, but if the AI finds your city and thinks it can take your city easily, I think it will usually try. So, you could move to the gold mine and build two more fighting units and a scout and expand afterwards. If you find a neighbor, you could send a delegation immediately and gift the 3 gold per turn and they might like you pretty quickly since that 3 gold helps every turn, I think.
When I was a little bit greener, I might have settled where he did. The reason why is I used to prioritize what is in the second ring a bit more than I do now. When I was greener than that, I would want to maximize the entire 3 rings of the city region. Now, I know that the first ring is critical in a deity game. Knowing that the capital, having the palace building, will expand to the second ring more quickly, but it still takes time and 2/1 tiles are not great. Food helps the empire expand more quickly. A very arid region, which sometimes is the luck of the draw, you might have 1 food tiles and that means you need 15 turns to grow. Often it will be a 1/3 tile so you can at least make some units, but I prefer a 2/1 to a 1/3 these days, because from turn one, with a 2/1, I can grow the city to size 2 and build a scout in 8 turns, and then I put two citizens on production to get a second settler and hopefully settle my next city near more food so I can start my loyalty pressure claim. If the cities remain low population, rivals can settle closer toward you if they are near. Building loyalty pressure is part of my opening strategy, and I try to do it if I can.
Of course, all of this analysis is after seeing him play and reading the thoughts of others. I can't say for sure what I would have done if this was my game, and it was completely fresh to me.