Protagonist, as your sources appear to have told you, doesn't mean the "good guy"; it means the "first actor", the character whose fate, whether success or defeat, is the central interest of the story. It's a structural role, not an ethical one.
The western dramatic tradition is full of villainous protagonists, from its earliest days (Clytemnestra in Aeschylus' Agamemnon) through the Elizabethans (the title roles in Marlowe's Tamburlaine and Shakespeare's Richard III and Macbeth) down to the moderns (Brecht's Arturo Ui).
The "bad guy" is frequently the protagonist of comedies, too: Subtle in Jonson's The Alchemist, Harpagon in Moliére's The Miser.
Antagonist, on the other hand, does not necessarily denote a dramatically central character. Some works provide a black-hearted villain who threatens the protagonist or whose goals the protagonist must thwart; in others, however, the force opposing the protagonist may be collective, and dramatically more or less colourless (Richmond in Richard III), may be impersonal (a god or Fate or, as Kenneth Burke has observed of O'Neill's Mourning Become Electra, really an aspect of the scene), may even be in some sense folded into the protagonist herself (Racine's Phédre).
Bottom line: You pretty much have to have a protagonist, both for dramatic interest and to attract a star actor. An antagonist is dispensable.
So there's always a protagonist (who is occasionally plural, as in Godot), good or evil or neither. If he has opponents there's no need to label them antagonists—you may call them simply opponents or rivals or whatever they happen to be. If he doesn't, you don't have to look for someone or something to fix that label on.