If it passed in its current form

It doesn't really have a "current" form.

An EU citizens initiative can really only outline what the goal is, and if passed, force the EU comission to investigate the problem to determine what an actual law could look like.

It would mostly harm always online live service models. This stuff only gets complicated if a game has micro-transactions, and therefore has to have a bunch of systems to handle payment and accounts.

If your game just does server-client/peer-to-peer multiplayer, like older games (and a lot of modern ones), there's barely any complexity to handle. Even less so if your game isn't online at all.

Basically every title on GOG would already comply with any law this might lead to. It's really not that demanding. The big publishers who nickle and dime their players are the only ones who would have a hard time. And that's a good thing.

If it passed in its current form, my fear is that it would effectively be an extra tax and burden just for choosing to make games instead of some other type of media, and I’m concerned investors would see it that way too, and move their financial support to these surer bets, ultimately harming individual game developers and lessening game releases.

But for most games, I don't think it would it be an extra burden? As an armchair developer, most games might do a DRM check online, which would have to get removed or emulated or something.

For multiplayer shooters, I don't know if dev hosted servers are somehow a lot easier to do, compared to dedicated servers of yore, even if they're just internal, and would get a public release when the game is EOL. Depending on how things are defined, a single player, offline mode against bots might also count and "just" the multiplayer aspect gets shut down.

Games that would have a harder time are probably MMOs or Live Service games. I don't know how those would get sold/made, if you can never shut down the game. Maybe those types of games would basically have to be rented or something, so it's explicitly clear you're not getting a perpetual license.