TL;DR:
From Airbnb Support: "You need not to register with local authorities as we have already done that for you."
Longer version:
I just chatted with Airbnb Support on this issue, since I'm traveling to China in a few weeks.
Initially, they gave me a bit of a brush-off, saying "we do not have any official statement about renting in china if the guests are required to register with local police or not so the best person to answer this will be your host."
I pushed back a bit, because Airbnb should absolutely have an official statement on this: the information we provide at booking either automatically registers us with police or doesn't. They should be able to answer that question.
The support guy contacted Airbnb China specifically to dig a bit deeper.
After confirming that I had filled out the "More information needed to pass to the Chinese government" page after booking, his response then was: "This was the registration part you were inquiring for and I am happy to share that you need not do anything when you arrive in China now as we will take care of the rest."
Because I'm thorough and I don't want to fall on the wrong side of the Chinese government, I made this explicit, asking him: "So to confirm: I do not need to register with the local authorities because Airbnb will do that automatically for me?"
His response: "Yes, you need not to register with local authorities as we have already done that for you."
