In the case you operate internet café where some of customers can use private room like this sample, you need to register your business with authority(警察署).
Because some persons try to commit crime by using computer in such space.
(even if you operate restaurant, if there is a such space, you need to register your business with authority)
However if your business is included in Hotel Inn, Lodge Business, this law is not applicable.
When you operate Internet Café, you need to inspect customer’s ID (passport, resident card, driving license) and make specified customer register and keep it for 3 years.
(However you can not copy of ID)
If customers make fake declaration, he/she will be sentenced to fine of 200,000 yen or less.
Moreover, if private room is completely lock room, your business may be included in entertainment and amusement business. So, you need to obtain permit from authority(風俗営業法).