I think the only part of what you describe that is potentially a vertical tie is the Unreal Marketplace license requiring that assets you buy only be used in Unreal.

Otherwise, you can put non-Unreal games on EGS, and you can put Unreal games on other stores. EGS does not give you benefits if you choose to publish an Unreal game on EGS, and I'd be surprised if all the games EGS buys exclusivity for are Unreal games.

Epic does sell their own games on Epic Game Store, but they also sell most of their games on Steam too (with the huge exception of Fortnite, though it's free to play)