Not really a game per se, but more of a possibility of a game mechanic:
I wonder if it would be possible to have a traditional antagonistic PvE encounter, in which both sides are played by players. That is, one side is a traditional group facing off against a powerful dungeon or raid boss, but that raid boss is controlled by a player themselves. Not aligned to PvP progression in any way, but mostly just... what would the result be if you had a human intelligence behind a raid boss' ability use?
Properly incentivizing both sides would be a problem. Well, the group has their usual incentive to win, but something has to exist to keep the Enemy from simply picking their nose while the group knocks over a loot pinata. Perhaps make it require a significant investment to queue up for the command encounter, to the degree that anyone queuing up does so out of selfishness for the rewards (so they have a strong incentive to win, otherwise they need to waste many hours/resources re-keying to become eligible to queue again). Probably reduced/secondary rewards for the loser in either case, maybe tiered for the Enemy if they put up a good show (if you could somehow categorize a "near loss" for example).
Maybe have some semi-autonomous nature to the encounter as well. Like, maybe you're not controlling just one unit, but a small group (think the various "council" fights seen in WoW) and you can hop between units to command them directly, or even hop out entirely and take a broader, tactical view...