Diplomacy can be brutal. You can force someone to accept your terms out of fear! Just think about Germany that annexed Austria and the Sudetes without firing a weapon before WW2, with basically France and England backing them, because they feared another war.
Yes, also, there could be a tenet (or the opener if openers exist) where they get tourism upon capturing a city, same way the Autocracy SP gave culture for conquering cities.
Also, autocracy makes taking cities easier, cities with great works, which would help for cultural victory as well.
Additionally, some kind of bonus for those artifacts of "historic battles" could make sense for Autocracy, and perhaps even a tourism yield from citadels, or certain buildings such the military academy, to play the influence through fear angle.
As for Order, in the current game it has quite a bit in terms of production bonuses. There could be an Order tenet that enables the construction of some kind of project or building that costs a good deal of hammers but increases tourism, or even a straight-up wonder bonus like the one in Tradition. The production bonuses will also naturally help build the standard tourism buildings as well.
Another tenet idea for Order is a tourism yield from either mines (less yield per) or forts (more yield per).
And for Freedom, there's no shortage of ideas there.
Keep in mind I haven't gotten to see the video yet so maybe some of these ideas have already been shot down