What kind of thinking skills are necessary to be a master of chess?

Chess thinking skills.  You have to learn how to think in chess terms.

Put in a general way, the logic of chess often isn't much more sophisticated than Wee Willie Keeler's "hit em where they ain't."And incidentally, memory has little to do with it either.  Mine is good.  But I have a friend--also a master--whose memory is like Swiss cheese.

planning intelligent strategy

Your intelligence outside of the game means nothing because only your knowledge of the game allows you to win

The analytical and problem solving only needs to be a average. Most Grand masters have a good memory as they just adapt previous played scenarios from other games by other masters.

They'll claim to strategists to sound cool / clever but it's nonsense. They won't think 5 moves ahead... mostly that's just trying to sound clever.

They play spontaneously like anyone else, but they play 5-8 hours a day when they're young.

When they play competitively they'll just play until they get stuck... Then they try to remember what previous game was played with the board at this current position and then adapt what previous match they think is best to use for the current game.

That's how Deep Blue beat Gary Kasparov. A computer can work out the moves that will be made and constantly adapt. Where as Kasparov could only think the computer was playing a strategy like a human.

I'm sure there was a rematch and technical Kasparov played the computer not chess. Meaning he played bluff moves to trick the computers programming rather than playing chess.

Forward and analytical thinking helps.

Logical and spatial thinking comes in very handy.

But a study of chessmasters have found that while they do tend to have higher than average reasoning skills and so forth, they were mostly outliers in terms of having exceptional memories. 

Which stands to reason since today, the game is so competitive and so much of it depends on knowing existing theory. 

For the more normal amateur, it seems to draw upon a whole range of talents, including logical and spatial thinking and, of course, a good memory helps. 

Chess also draws on intuition (which may be closely associated to memory - something tells me in this position, you have to do this, but I'm not quite sure why), imagination, creativity in its own way… the ability to imagine how position A could turn into position B.

People who think in a logical, methodical, organized fashion tend to do well. 

There are also other skills that will help the competition player, which include patience, self-control, objectivity, etc...

Have a plan of strategy ahead of time, react when you see their strategy or opening, always guard your strongest pieces (King, Queen, Rook, and Knight --- In that order,...maybe), don't let your guard down, only expose the weakest pieces. Set them up for a fall-into trap. Try to get rid of their queen as soon as possible. Though, I lose more games than I win anyways, so why would you listen to me? Still makes sense though right? Maybe you can use my system better than I.

Allot of experiences can help. 

i think any type of thinking skills would help

A bit of logic, a bit of knowledge, a bit of strategy, a bit of tactics and knowing how to think one move ahead of your opponent.

Oh, and to remember to check what your opponent can do.