The itch.io desktop app is open souce, but afaik the website isn't. It does actually allow devs to get paid though, through charges or encouraged donations. There are some games you can get from flathub or the standard linux package managers, but they don't have any built in features to pay devs.
https://flathub.org/apps/category/game
The expensive part of hosting game files, pages, and mods isn't really any different from what flathub or similar already does. I suppose cloud saves would require extra storage space, but I'd imagine an open source game store could charge for their cloud while also allowing p2p or a selfhosted cloud, which is a similar model to what a lot of open source projects with cloud features already do. That would be a fairly sustainable monetization scheme for the store I think, especially with donations on top of that.
Devs can be paid partially through donations, although I doubt that would be nearly enough without a system like Itch.io has where it always shows a payment screen that you have to click through before you can download the game. There are a couple more models, ArmorPaint is open source but you have to pay for binaries or compile it yourself, and Aesprite is source available (restrictive license) but takes a similar model. Overall though I don't think open source games will ever become the standard, even for indie devs, and even if open source platforms do.
he's like xkcd.com/1112