First of all, the games ARE part of the Cross-Time, being referenced in the show itself.
Next, the head writer of these games have not just been a head writer of the show itself as well, but the games have been written to work under the same narrative and logic of the Prime Timeline, being able to fit in it, even tho not being "Canon", just as everything else written by her.
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https://archive.is/QfIKw
So, the games work under the same logic and powerlevel of the Prime Timeline in a narrative way, and they're are indeed part of the lesser Multiverse.