Character Role Analysis
King Pentheus bears all the hallmarks of an antagonist. The easiest way to figure out who fills this role is to first ask yourself, "What does the protagonist want?" Then ask, "Who's standing the way of that thing?" It's pretty clear that Pentheus is the force that Dionysus is up against. He's the guy standing in the way of the god's attempt to spread his new religion.
We'd also just like to point out that as antagonists go Pentheus is pretty weak. He's got nothing on, say, Lord Voldemort or Darth Vader. Ultimately he's just not a particularly tough adversary for Dionysus. We're not trying to diss on him or anything, he's just made the unfortunate decision to antagonize a god. There's just not a whole lot a mortal can do in the face of divine power.
Also, though Pentheus is kind of jerk sometimes he's not much of a "bad guy." Sure he's bullheaded and he's got a temper, but ultimately he's just trying to keep his city from falling into chaos. Pentheus is just trying to be a good king. Pentheus is a great example of how not all antagonists necessarily have to be ill intentioned.