Note: I'm not asking if the Multiverse Theory and the MWI are the same thing, cf. e.g. this Phys.SE post.
If I understand it correctly, the Multiverse Theory doesn't rely on the Many Worlds Interpretation. Is my understanding correct, or does the Multiverse Theory relies on the Many Worlds Interpretation?
If it doesn't rely on the MWI, does it rely anyhow on Superposition?
If it doesn't, does the theory even "belong" to Quantum Mechanics?
I appreciate the help.
The linked multiverse theory is just a general supposition that there are other universes that follow different rules.
The many worlds interpretation, a separate idea, is specifically with regard to quantum mechanics, and interprets superposition as indicating that there is a world associated with each possible outcome.
Seeing that there could be different rules of quantum mechanics there can therefore be multiple universes which all have their own "many worlds" of their own versions of quantum mechanics. Therefore this general idea of there being other worlds with different laws of physics is sometimes thought to be a bigger multiverse than the many worlds interpretation, as described in the wiki article you linked.
The multiverse idea you have linked could have been supposed before quantum mechanics in the days of classical physics by just supposing there are other worlds with other rules of physics -- and isn't necessarily connected to superposition.
Everett's many worlds interpretation though is a specific interpretation of quantum mechanics and is very much associated with superposition.
