I think annihilation is a property of how we played the game and not of the game itself. I get that the game was designed around it, but there's nothing stopping players in a Free For All from subduing an enemy into slavery instead of wiping them out, some may call this an ally. In fact, it's probably the optimal strategy, annihilating might be a pyrrhic victory, where one player is knocked out, and the 'victor' is left with half an army. The only winner in that situation are the rest of the players who are now better than the two players.

Except NvN games, I except FFA and 2v2v2v2 games to show elements of empires, it's only games with two sides where minmax becomes a viable strategy and damaging the enemy is the same as strengthening yourself.

That's how my friends and I play Civ. We had an issue in the beginning with players getting knocked out in the first day of a game that might go for 5 or more play sessions, so we devised a scheme where a player could be forced into vassalage. They can no longer win outright, they merely exist to support the conqueror. The conqueror gets to overrule any decisions made by the vassal, but there's a bit of a gentleman's agreement that this power should be used sparingly, since it's annoying to be micromanaged, and it slows the game to a crawl. In particularly aggro games, the same vassal might be handed back and forth between two players still in the fight several times, because as a relatively underdeveloped nation, they represent a fair peace settlement.

Civilization (at least 4) also has subjugation as an explicit mechanic where a mostly defeated AI state surrenders as your vassal and has to give you resources, vote for you in UN elections, fight in your wars, etc. but they otherwise continue to act independently.

I think this is unlikely to happen (or at least, be sustained very long) in most games because being a slave to another player doesn't sound very fun. Playing as someone else's vassal (and being deprived of any real chance at victory) would be tedious and probably slightly embarrassing. You'd rather just go out of the game, and if in the process you end up screwing over the player who beat you, all the better.

Two powerful players can decide to cease hostilities in order for each to preserve their own ability to ultimately win the game, but if one player's ability to win has been irreparably compromised, then they will probably just fight to the last man in a way that real civilisations pretty much never do.