A game today which is struggling to accomplish this is Star Citizen, and they did a video on what they plan to do here:
https://youtu.be/TSzUWl4r2rUAnyways, I think the big challenge compared to real time apps like Google docs is that game simulation is significantly more complex than synchronizing bits of text. One problem is that at a minimum, you have the round trip to the server as latency between “submit command” and “receive simulation result”. And this has to happen many times per second so that it looks realistic. And then on the server, it has to be processing the changes from N connected players M times per second, and then simulate what happens in the universe. And if simulation (M) drops too low, you get desync problems where players are rubber-banding and the AI gets very dumb. (An example is that star citizen appears to have great AI in demos, but in the live server, the servers can’t process changes fast enough for the AI to work well.)
And then, if you want a lot of connected players or a big universe, this just gets more and more complex, and you’ll eventually out-grow the ability of a single server to process changes. At which point you also need to handled data replication among multiple servers. For example, star citizen game servers don’t have capacity for more planets at the moment, either because of memory or cpu constraints. So sharding the universe into multiple servers is a pre-req for the next stage.
So to more directly answer your question, it’s definitely possible to implement. Many games have basic versions working. Minecraft is an example, but it can’t scale to hundreds/thousands of players. New World is another recent example, but even its servers have player caps. No Man’s Sky is sort of an example, but it keeps players spread out so that they rarely encounter each other. Eve Online is also an example, but I think it reduces the amount of nitty-gritty simulation details. (So it might not have a very in-depth physics simulation, or first-person-level details.)
So it’s basically a scaling problem, and even then still has limitations based on the speed of light (for internet latency) which limit how good it can get.