Thanks! I should have been more precise and said that each player's LiveView socket is a separate process, and each game is a PubSub topic. But yes, games are persisted in a database after each move so you can close the window, come back later, re-join on your phone, etc, just like you'd be able to do on chess.com. So games that are abandoned currently stick around in the database, but don't keep a long-running process up unless someone actually has their browser open the whole time. Games with a timer (regular games that were started with a per-move timer and all tournament games) eventually time out in a loss for the player who let the clock run out, but those stick around as well - you can view replays of any finished game.
Deploys and restarts don't impact too much - sockets just reconnect and the state reloads from the db.
This is a great point, having experienced just this firsthand just recently. I launched an online boardgame and tried announcing it in a bunch of different places - boardgamegeek, some relevant subreddits, elixirforum. While the other forums got views, the one that actually got some real engagement and comments was the boardgamegeek forum, arguably the "crappy" one of the three. Although it's "crappy" only in the sense that it's pretty no-frills and just feels kind of old-school.
The unfortunate thing is that there actually already is a government mechanism for this, in the US at least, but it's been lobbied against by the industry [0]. So like, there already is a way to do this, the same way that libraries are allowed to preserve copies of every book, but the video game industry blocks it from happening.