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The IP address on hand is probably the hotel's public address used for NAT, especially in 2012. This means you'd need to have full NAT logs + source port + something like a captive portal setup that forces the user to identify the room to be able to tie (externalIp, sourcePort) to (user, room). The captive portal type isn't unheard of for hotels, even in 2012, but the NAT logs... it's no surprise they had to ask for the room list.

With IPv4 there's zero chance of that. At most, you could get all the people who were using [Gmail] around that time. With IPv6, mayyybe, but that assumes the hotel does as much data collection as possible and does it correctly.

Assuming the hotel had customer specific login info and the person you are looking for was using it, sure.