Has anyone else noticed a Rock/Paper/Scissors similarity to various chess playstyles?

It seems to me that chess players can be catogorized into 3 main playstyles, and each seems to be strong against one of the other styles, and weak against the remaining style.

Paper -

Players who use the paper style are strong defensive players that erect a veritable fortress with their chessmen; each piece carefully placed in relation to the others, typically behind a secure pawn line. Of all styles, paper players have the most proficient pawn moves. They easily absorb all but carefully calculated attacks, and coil, waiting to strike when their opponent makes a mistake. These players are more inclined then practitioners of the other styles to sacrifice material for positional advantages, but also tend to avoid trades, preferring instead closed, quiet games involving lots of positional maneuvering. 

favored chessman- pawn.

Scissors -

Precise and elegant, scissors style players are strategic masters who perhaps best embody the "art" of chess. If they see an opportunity, they'll line up a subtle attack several moves down the line, but which is nigh unstoppable when the trap is sprung or the noose finally jerked tight. They tend to slice through Paper's defenses with relative ease. These players live for finding midgame checkmates, but perform particulary well in the endgame, where their far-reaching foresight works to their advantage and Rock's attacks are fewer and farther between... provided they still have time on the clock. These players are the ones most likely to run out their clocks during a game, and gain an increasingly favorable advantage the more time they have.

favored chessman- minor pieces

Rock-

Best suited for blitz play, Rock is highly aggressive, making immediate, bold attacks whenever possible. Rock prefers to trade pawns early in the opening, both because pawn play is a weakness for this player, and because he prefers an open board that allows for long-range attacks. He is more likely to prefer material to position than the other playstyles, but above all else, his goal is to seize and maintain the initiative, keeping his opponent in a state of constant reaction, and paying little heed to his own defences save for security against immediate threats. Paper players wait for Rock to overextend himself as he bashes uselessly against their secure defences, and are usually rewarded for their patience. Scissors laughs at Rock as one might laugh at a person who brings a baseball bat to a fencing match... until their rapier lies twisted and broken at their feet, unable to cope with the bat's speed and strong, unrelenting bashes. Scissors players can usually deflect or sidestep Rock's attacks in annoyance in the short term, but over time find themselves with their strategic positioning in tatters and facing down multiple aggressive enemy pieces in their own territory. They leave the game frustrated that their superior technique was bested by crude aggression. Rock tends to dispise endgames; he lacks the foresight needed for endgame precision, competency in pawn play, and the pieces he earlier used for his attacks.

favored chessmen- major pieces

Do you consider this a useful analogy? Have you seen this pattern yourself in your own play? Which playstyle do you prefer? How would you categorize some of the current chess champions?

if a person is scared and tense they usually avoid opening their hand

It's an interesting idea, and I think it has a little truth to it.

But for example, someone who just defends can be in trouble vs an attack if their pieces end up too passive. This only make the attacker's position stronger because they'll be free to shift to other part of the board.

And attack vs elegant play can fail in positions where an attack isn't the correct idea. If the attacking player tries to force it to work it will just backfire against a solid positional type player. 

In my opinion, these characterizations are way to simple to be useful. For example there are certainly attacking players who do great with minor pieces. Likewise there are aggressive players who do quite well at long time controls.

There are certainly people who like closed positions. If they are actually successful with that style, they are going to be quite good with positioning their pieces for optimal effect as well.

Also in general one dimensional players are just that - one dimensional. Really good players are comfortable playing many different types of positions.

If you listen to aggressive attacking GMs like Simon Williams, he makes it clear that any grand master has to be good at end games. There are times where going into an end game is simply best, and at that point, attacking player or not, you need to be able to play it.

In chess there  are only 2 types of moves, good moves and bad moves

you cannot defend without attacking