A must read:
https://www.gnu.org/philosophy/free-sw.html
List of free as in freedom games:
https://libregamewiki.org/List_of_games
I personally think 0 A.D is one of the best games produced by the foss community, you should take a look into it.
Apart from that, there is a need for more development in free FPS games.
EDIT: Actually, every genre needs more development, like racing etc. But most people play FPS games and so I thought it would be best to suggest that.
Ah I forgot, yes this has been done before, multiple times even, for example there are: http://www.playdeb.net/updates/ubuntu/17.04/ which is kinda like Steam but for Ubuntu. And there is: https://lutris.net/ Which is more of a game manager like Steam so you can also install proprietary games with it. And you have of course the build in packet managers in several Linux distributions which is I think the way to go since it is most convenient for Linux users, just type "install game-xyz" and you are done. There are also several more failed projects I think which I currently forgot.