How does this relate to the many-worlds interpretation?

There is a surface resemblance: the multiway system has many coexisting branches that look like parallel universes. But Wolfram's model claims something many-worlds does not — that causal invariance forces diverging branches to re-merge, so the branches are not permanently separate worlds but points in an emergent branchial space whose geometry is meant to encode entanglement. This is the model's own proposal and re-interpretation, not a derivation of standard quantum mechanics or an experimentally confirmed result.