How do they feed the game screen to the models? I imagine the models are too slow if you send 60FPS, but I feel like that’s also the case if you maybe feed it 1FPS? If you go any slower, you’ll miss too much info?

I would assume it's pull-based so the agent takes a screenshot whenever it finishes a turn.

Essentially yes. For games with some real-time component (FFVII), the game pauses after actions are executed to take a screenshot and let the agent think.