He means the whole game. It should be a playback where you can pause the GIF to watch moves in more detail.
Is there a way to make a gif of a 4 player chess game?

I would assume they’re talking about something similar to with how you can download gifs of your live chess games after you’ve completed them; GIFs cannot be paused, so unless 4PC is able to handle the lag created by making MP4 (actual video files), I would assume that GIFs would be implemented if this idea is accepted.
Being able to make 4 player chess gifs make it easier to share the game to people without chess.com accounts.