Yes - there are pretty regular thematic tournaments here. In fact, if you look under the tournamnets "tab", you'll see a Colle-Zuckertort tournament and a Scandanavian defense tournament taking entrants right now. Most of the time, the admins are pretty responsive to requests, too, so if you really want a "Italian game" tournament, you can post here or send feedback and usually one comes along fairly quickly.
Of course, you have to subscribe to play in tournaments...