"Protagonist" doesn't necessarily have a positive judgment attached to it, does it? I.e. if the main player in a story is the bad guy, we still say "protagonist"?

Not sure, but in a good vs evil story I think it does. I naturally assumed due to the implucation of an antagonist a protagonist always meant the subject of the conflict (every plot has a conflict they say). But you might be right, I can see how it can simply mean the center of a story.