I fit all of those, so I guess I must agree ;). As per the strategy games, don't forget Go, an ancient chinese game that can take literally forever and taxes the mind incredibly.
Also, in response to the original post, while I like to think that I brought a good deal of logical thinking to the field when I learned Perl, I often find myself solving problems in my head in Perl (not just coding problems). After long enough, you begin to think in Perl as you do in your native language.