I decided to do one final game where I went complete warmonger. Rushing the Huns->Mongols combo I was able to steamroll every other player on my continent, and the slow tech pace of the Ai meant they lasted until about the last 10 turns of the game, when I upgraded them "because I cuild." Don't think it was really needed to win. (Pretty sure his was on Nation Difficulty, although my options screen says it is Humankind so I don't know, AI units didn't have their combat bonuses)

I accidentially discovered that the influence cost of being over the city cap, and the resulting influence deficit is pretty unconsequential when you can just conquer cities instead of founding them. Long story short, I hit the industrial techs for coal and oil around turn 120 and 130. Not that it mattered much since Mongol Hordes could grow on their own without needing my empire, and they easily owerpowered the swordsmen/archer stacks I was facing.

I decided to pivot into an extermination game once my army grew large enough, After dozens of wars where I chipped of a city or two each of the AI, releasing them as independtents when I was done killing their original owner completely, I finally got the last AI player down to nothing. Exterminating them, to my dissapointment, only gave me a gloving "next turn" button. No rewards or end screen.

Is complete elimination of all other players not meant to be a victory condition? Or was that simply not added to the beta version because it was not expected that anyone would try?

the only victory condition is fame

I get the impression that Fame/score/time is meant to be the only win condition

The devs have already stated that to win you need to have the most fame by the time the game ends. As Fame is the only win condition. However there are supposedly, as mentioned by a dev on reddit, a number of game ending conditions (none being winning conditions) on launch.

If the game in this closed beta were to have ended the moment you eliminated the last player, and it would turn out you had less fame than another eliminated player, you would come in second place.