Privacy Concern: Details website owner

I received today an email from Z*nga G*me N*tw*rk, the owners from a well known f*ceb*ok game asking me to remove my website since I'm promoting a CB product for it.

I agree with them and will take it down, however they must have been looking up my personal information to find my personal email address. Now I'm not sure how this works, but for example in my country when a parking officer gives you a ticket and looks up after your information, you can sue them because they are violating your privacy. Could I do the same here?

If you information is available in the public domain, it's fair game i'm afraid.
Something else to bear in mind is that law enforcement & government agencies have to play by the rules (LOL.....quiet chuckle) so they have to go through correct channels when requesting information (sometimes, even if it is already available in the public domain). The reason being is because they have to be able to provenance the information obtained in a court.
In some countries it's illegal to rifle through your neighbours bins & obtain personal information, in others it's not....funny old world we live in.
In a nutshell though, if they have obtained your information through publically available records then there's nothing you can do other than drop off the grid (that's nigh on impossible).
You could always respond with a request to establish from where they provenanced your personal information.