The inside size of the chain is, give-or-take, the same 8sp, 9sp, 10sp.
It's the sideplates, rivets, etc which allow the chain to be narrower.
So no worries that the chainset teeth won't go through the chain, it's perfectly wide enough.
Rather, the concern might be that the rings are too far apart and the chain could drop between them, but that actually won't happen either, the chain isn't externally so extremely much narrower either.