>Which, in a game, should be the group.
Not in the vast majority of games, no. It's perfectly possible to make a game where the group do not drive the plot forward, and be thoroughly enjoyable.
>Because the group decides where to go and what to do, setting the tone and pace of the game
Which is not the plot.
> if the group decided that they don't want to be mercenaries of a kingdom in civil war anymore and instead become bounty hunters in an empire next door, then they are the protagonists of the story, not the king who won't be relevant anymore.
Because yes, they're the focal characters. But that strand of plot, of the kingdom in its civil war, which is now proceeding however it would go once the PCs leave, can survive and proceed quite fine without the allegedly protagonist PCs. It's just that you've stopped paying attention to it, because the focus went elsewhere.
>The villain, in literature and other art forms, is generally called 'antagonist'
Not necessarily. For instance, Iago in Othello is definitely a villain, and is definitely the protagonist. He makes everything happen, he has the most lines, but yeah, he's the bad guy. The titular Othello isn't really a protagonist in his own play.
>Not really, the antagonist can still be the same. And because it's Veeky Forums, I'm going to take Jojo as an example: the protagonist is not Dio, in either the first or the third season. It's Jojo and his group of world-savers.
I've not seen the show so I can't comment on it.