That post is dumb.

The act that truly cements Gaston as the "villain" of the story is when (in what I think is the movie's best song), he rallies the entire town to go kill the beast, now at this point in the story, the beast had attacked and kidnapped Belle's father, and he also held Belle hostage during which he verbally abused her, kept her locked in her room, and even came close to physically assaulting her.

He didn't believe Maurice at first. Saying that he wanted to go and seek vengeance on Maurice's behalf is dumb. He even used the story as evidence that Maurice was crazy to throw him in an insane asylum unless Belle married him. He's not even interested in Belle as a person, he wants her to make babies and rub his feet, and damn her own interests and desires.

The second point is just as dumb too. He made multiple attempts in to the movie to get her hand and she said no. He still shows up at her house, invites himself in, tells the whole village they're going to wed, and then pisses all over her interests, insults her intelligence, and then plots revenge when she kicks him out. That revenge takes the form of, as mentioned, a plot to throw Maurice into an insane aslyum unless she marries him.

The whole rest of the post is equally dumb because it makes an incredibly stretched argument that only works if the film wasn't told from an omnipotent point of view. Yes, Gaston would have been a tragic hero if all we saw was his perspective, but we don't. We, the audience, know that the Beast is a good guy, that Gaston is a jerk, and that Gaston wants to kill the Beast solely to knock him out of the running for Belle's heart.

He's not a villain in the way Scar or Ursula are, but he's still the villain of the piece.