We know Rumple and WRumple share the same Darkness. So, if Rumple loses his Darkness inside him, so does WRumple. I understand that part. I also get where WHenry took away Rumple’s powers and immortality yet he was still the Dark One. The Darkness inside him still resided. So did WRumple.
But all the complications occur after Rumple takes his heart out. What happens after that? His heart was cleared of the Darkness somehow. But why? Also, why did WRumple die even though only his shared Darkness was destroyed? There is no connection between his life and real Rumple after all. Just like Snow and WSnow. He should not have died.
If you accept that they share the same Darkness, etc, the question is: Why did Wish Rumple die?
Wish People aren’t connected in life force (though they can be in other magical means). Wish Rumple crumbled to dust for no other reason than...he was completely consumed by darkness.
Once Wish Rumple lost both Bae and Belle, there was no light left in him, so he simply crumbled to dust. (Also, it’s just a show thing to not have a literal comatose-like corpse on the ground when you could use magic, akin to Serum Queen, who did as her heart did, though she reformed.)
So, to give another example, take Henry as Author. If he died, the Quil would move on to somebody new and not recognize Wish Henry (possibly). So, the Wish Quill (because they never said what happened to the real one) recognized Henry because magic crosses even these reality barriers.
My personal opinion is that Wish Realm Rumplestiltskin's death was a consequence of the Darkness being destroyed (the "price" of the destruction of the Darkness, in a sense). From the events of the episode, it appears that if the power of Darkness is destroyed, anyone who is currently a Dark One will also die with the Darkness. The episode makes it quite clear that Weaver/Rumplestiltskin's sacrifice destroyed the power of Darkness, but since WR Rumplestiltskin was still a Dark One even after the original Rumple had "purified" his heart, he ended up being destroyed. Excalibur would have circumvented this issue, because that sword has the power to draw the power of Darkness out of every Dark One (thus also negating their status as Dark Ones), but without Excalibur to perform this extraction, destroying the power of Darkness also seems to kill all active Dark Ones as well. If this is true, back in Season 5, if Emma Swan or someone else managed to destroy the Darkness before removing it from both Emma and Hook, then Emma and Hook would have died at the moment of the Darkness' destruction.