Beware this misleading reply!
While this might have been accurate in 2016, since mid-2018 Airbnb hosts in Japan have the same guest registration requirements as any other accommodation providers, such as hotels, hostels and ryokan. That means they need to collect personal information such as name, passport number, address, occupation and a copy of the passport page for each guest. Because Airbnb listings won't have a front desk to collect that information when a guest checks in, hosts will usually ask for it in advance.
As a host in Osaka, Japan, I am very familiar with the process. It's a pain, and I wish we didn't have to bother guests for this sensitive information. But it's the law, and we risk deregistration and massive fines if we don't comply.
Here's is a list of the requirements written on the Ministry of Health, Labour and Welfare website:
https://www.mhlw.go.jp/english/topics/lodging/index.html
