I have to agree with Nikitas it is a common European practice .
Many years ago ( before the EU) you would also have to fill in a police questionnaire too ~~ in fact it was quite strange to sit down to dinner and see the police with our passports obviously in their hand reading the slip of paper with my details on and looking you up and down ~ what exactly they achieved doing that I don't know.
France
and all of the Eastern block countries seemed the worst
I've never heard of it being done in Cyprus though.
I've just recently spent a few weeks in Italy ~ mainly to visit old friends and the rest of the time was spent touring around the country.
We stayed in a lot of hotels mostly 4 star and they all except one asked for my passport ~ the only exception was a 5 star hotel right in the deep south of the country and they only required a scan of my credit card .
Although I didn't give up my passport I did leave with them my Cyprus ID card and they seemed reasonably happy with that.
As I mentioned I've never heard of it being done in Cyprus so I would check with the CTO as to whether the information you found is indeed true.
Bill