Oh boy, I was thinkin a thing about this game earlier today but there were no recent threads to post it in.
SO
I think the "other world" in this game isn't the Dark World. Rather, I think it might be a "what if" world. It's already a what-if timeline branch anyway. What if Link in LTTP hadn't defeated Ganon? His evil would have spread out from the Dark World and transformed the Light World into a similar hellscape. The Triforce would have remained under his power, and maybe... become blackened with evil?
There's gotta be a reason they don't call it the Dark World, and the method for entering it sure is different than it was in LTTP. If it's not a what-if Light World, maybe it's a future version of the world, one where Ganon comes back and fucks the place up? Either way though, I think it's a "polluted Light World," not the traditional Dark World.
Maybe.