Is chess just a game of memorization and study?

You may think of a chess board and it's pieces as a blank slate where you can make any move and become victorious but is it? Aren't the pieces all worth a certain amount due to it's versatility and how the game functions? Hasn't it created a game that must be played a certain way or else you will lose? You must open with a real opening or you will most likely lose. You must castle early, you must not bring out your queen too early, you must fianchetto the bishop, fork with the knight, etc. (most of the time). You learn from other's but when you start doing what's not being told in an extreme fashion you are losing. It's like if you are disproving 1+1=2 you are falling in a pit. You must gather advice + techniques see how it plays out for you. You must study the lines and memorize play sequence. 

Where is the real brain work going on?

Part of what makes chess fun is there are exceptions to every rule. To use your example of castling, in some games it's a mistake to castle! The king is better in the center.

But before it's possible to learn how to break these basic rules, you have to learn the rules to begin with. If you keep your king in the center for no reason, then yes, in most games you will lose.

However, the constraints add depth, not take it away. A writer must use words, must use certain archetypal characters, settings, story arcs. A painter must use certain complimentary colors, shapes, contrast, must use the canvas, etc.

Total freedom means no depth, no creativity.

As for knowing openings and strategies and asking what is there for the brain to work on, it's a similar story. Think of trying to play an instrument you've never seen. Or speak a language you've never heard. Total ignorance means there's nothing for the brain to do. After you learn the structures, patterns, rules, and exceptions to the rules, that's when there's intellectual depth. That's when there's invention, exploration, and creativity.

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However I sympathize with the feeling. Non-players often think of chess as a test of raw intelligence. However it's not. Chess is more like a musical instrument, a sport, or an art. A game is a performance by two players who have spent countless hours improving their craft. An artist doesn't amaze the audience with a new color. sound, or character but on a subtle variation, an unexpected twist, a genius addition or subtraction of an idea which seems impossible at first.

Chess isn't as rigid as you're making it sound. We've invented general principles to help us find our way through the maze but they're really only suggestions.
If you play a bad opening then you've played bad moves and you opponent should punish you with correct play but there's lots of room to play sound offbeat stuff.
Ultimately a position is either won, lost or drawn, and today's top players are pushing the boundaries and playing in ways that weren't thought legitimate decades ago.
Chess is an art. It takes artful skill to create attacks and carry them out with good timing, find defensive resources and different ideas, and in general correctly interpret the board to move the pieces most effectively.
My longest chess rant ever.

Nicely put mr Chin 

Memorization and study?,  Yes, there is a lot of both of those going on 

Chess is a  practical example of a field  of mathematics known as Game Theory.  In other words, Game Theory mathematics is the wire frame for chess.

I am no expert on  how  chess engines work or how it is  they  play chess so well.  I will take a stab  at it.  Boolean Algebra is applied  to game theory mathematics and the particular rules of the game.  In other words,  a computer working model of chess.

Where is the real brain work going on?

There are billions of possible positions in chess.  The real brain work goes on when one of those positions appears on the chess board, and  a chess player has to analyze it with  the thousands of visualization pattern memory banks in his brain in order to determine the most appropriate  candidate move(s) that will at  least equalize the position.  And, then select the one candidate move that will at least re-establish  the balance in the position.

Except for the botched computer chess engine explanation, I hope this answers your question.  The answer in my opinion is no, chess is not just a game of memorization and study.