I've exported 3D models from the game, can I print them? Assuming I've extracted 3D models from a game which I legally bought (such as StarCraft). I am allowed to 3D print them for personal use or give it to close friends?

Is there any general rule, or this suppose to be specified in the license? If so, which section/clause potentially can prevent me from doing that? Or I need to contact the company who owns the game to obtain the permission?
No. Such figures are generally covered by copyright, which means that nobody but the copyright holder is allowed to (re-)produce copies of the work. Copyright also covers personal use. In the US there are limited fair use exceptions but they do not apply here.

The only way to do this legally is if it is specifically authorized in a license or if you get permission.