Google already complies with that except the default is one big switch AFAIK on android, it's not per-category.
So if you install something say from Fdroid and want to have it up to date (say a Firefox rebuild), you have to periodically open the Fdroid app, check if there are any updates for the app and manually install them if there are some.
Also I don't think you can currently hide Google Play if its installed, again giving it an unfair advantage.
I think the intention is to prevent Apple saying "either you use our store exclusively, or you opt out of all our apps".
Google lets you install a browser from one store, a game from another, and everything else from the official Play Store.
Google could also easily implement category switching. The URL navigation structure of android could just append ?cat=gaming.