It's a clone of https://generals.io/
It's built with LiveSvelte. It doesn't need any predictive features as it's basically a board game and runs at 2 ticks per second. It does use optimistic updates to show game state before it actually updates on the server. The server overrides the game state if they're not in sync.
All game logic is done inside Elixir. To do predictive correctly, you'd need to share logic between the server and the client. Otherwise you're writing your logic twice and that's just a recipe for disaster.
One possible solution which I didn't investigate, but should work, is to write all game logic in gleam (https://gleam.run/). Gleam is compatible with Elixir, AND it also can compile to js, so you could in theory run the same code on the server and the client.
Now this is a big mess to understand, you could say "why don't write it all in js and be done with it" and you'd make a very good point and I'd probably agree. The main advantage you get is that you can use the BEAM and all it's very nice features, especially when it comes to real time distributed systems. It's perfect for multiplayer games, as long as you don't take into account the frontend :)