I travel to Italy regularly. While it is true that hotels always used to require to see and photocopy your passport, I would say that in 50% of my stays that no longer happens. Either the law has relaxed, or the hotels themselves have decided not always to bother. I also suspect that guests in Europe with European Union passports might be exempt now..
No that's not the reason in either case. In your case either they have stored your information (most likely) or they have (a very very rare occurrence) forgotten to ask...but I doubt the latter.
I have stayed in literally hundreds of hotels in Italy and not once have they not asked me for ID. If anything the immigration laws are more enforced these days there.
As for European guests there is no exemption whatsoever. They (we) have to show ID each and every time. That would be a major employee infraction so it is second nature to check-in staff.