Tennis certainly has a mind-game component, but it's smaller, I believe, because you're reacting intuitively, you simply don't have the time for mind games, unless those at the press conference where you tell everyone that you've barely been able to train.
> I don't see any "reaction time" available in RPS (considering equal in matter of body), and no way to predict the choice of the other one (as you stated) so similar to coin toss (you can't influence the choice of the opponent).
But you do have ways to predict the choice of your opponent. You "just" need to understand how they think. If you chose rock and they chose scissors, what will they choose next? Are they the type that figures "he will choose rock again, I'm going to pick paper", or are they thinking "he will try to mix it up and pic scissors because he thinks I'm going to react to rock by using paper, I'll take rock"?
If you played against a computer that just used a perfect random number generator, I'd agree with you. But you're playing a human, and they're terrible at being random.
It would be absolutely a game of luck if you played one game against one person without knowing who they are. But since, similar to Poker, you can learn over multiple rounds, the luck quickly fades. And apparently, if you're playing the odds, many people will start with certain choices, and they don't pick each choice at the same rate. There are quite a few articles (and books) out there, and they often mention the World Rock Paper Scissors Society, which also holds international tournaments.