Of course people ask for a rematch. For some, it might be vindictiveness.
But for others I think it is more of a matter of the wanting to know, in some numerical way, who is the better player.
You need at least 2 games before the players will generally accept which of the 2 is the better player.
Personally, I only consider rematches if 1) It was an interesting game, 2) I lost because of a really stupid blunder. For me, it is not about vindictiveness but for the sake of competition.
Whether chess creates vindictiveness/ruthlessness in you?
Why I ask this question is that whenever I checkmate my opponent some people ask for rematch, I guess, to take revenge.
For me, I admit, to some extent playing chess makes me vindictive.