I don't see "game" mentioned in the wiki at all. Is that something typically used for games or do they tend to use something else?

Collaborative text editing is what it’s traditionally used for.

It can also be used to mutate hard game state (I wouldn't try it with dynamic, interpolated values like object position, angle, acceleration, or velocity.)

There are many other methods, some are more precise and compressible than others:

Trailing State Synchronization

https://www.cs.ubc.ca/~krasic/cpsc538a/summaries/38/

Basic ideas

https://www.gafferongames.com/post/state_synchronization/

https://engineering.monstar-lab.com/2021/02/09/Game-server-S...

https://www.gabrielgambetta.com/client-side-prediction-serve...