
Those chess boxing folks are serious! I think I'll start my own hybrid sport where people have to spontaneously make poetry while doing "Tae Bo".
As a former high school chess nerd, I can respond to some of the points. First, there are lots and lots of books on chess theory. More than any non chess addict would ever guess. If you want to get good at chess, you need to study chess and then play some. You'll spend way more time studying than playing. In the case of openings, most serious players just buy a book outlining the most favorable openings and memorize the first few moves and variants. When I was serious at it, my standard openings as black were Sicilian - usually dragon variation and Grunfeld. As white, I always opened Bird's. I chose these because they are unusual so most others wouldn't know them and they are all hypermodern - leading to open games which lends itself to strategic thinking which is easy for me.
A few years ago, I met a guy at work who was a serious chess player - did ranked tournaments etc. I hadn't played chess in years. He played me thinking it would be easy and I ended up beating him several times in a row. (Then he stopped asking me to play chess.) The reason is that I had somehow internalized the principles of chess on the same principles I use to fight. I play chess like I fight and somehow it makes sense for me to think about it that way. Here are some principles common to both fighting and chess:
1) Advantage is gained by controlling space and limiting your opponents.
2) Doing the unexpected can cause paralysis and mistakes on the part of your opponent.
3) Keep a strong structure (body mechanics or pawns as the case may be)
4) Timing is critical. If you can't hit somebody, try to make him waste his energy. (this is the concept of "tempo" in chess)
5) Defend and build up your strengths, not your weaknesses. (For example, if you are a great hitter, then learn to hit even harder. Witness the success of this in the Liddell, Couture fight. The winning solution for the striker was not to cross train into BJJ and become a wrestler, but to turn the guys face into hamburger in a dozen hits or less.)
6) Use complexity as a weapon. (In fighting, this means doing things which require elaborate counters on the part of your opponent. In chess, this means choosing lines of play which require your opponent to spend a lot of time thinking about all the possibilities.)
7) Use deception. (Choke a guy to get him thinking about his neck, then knee him. Kick at his legs, then hit him in the head. In chess, there are all kinds of traps and sacrifices. Pull a few in a game and the guy gets gun-shy and starts playing too conservative.)

Always remember you are fighting a person, not playing a game. (Bobby Fischer made great use of this. He tried super aggressive stuff with tricks and traps. His opponents started having nervous breakdowns. They couldn't take the pressure. It didn't matter if the technique could have been defeated by a computer playing chess. Bobby was fighting his opponent using chess as the medium. In physical fighting, always remember that when the brain panics, the body stops fighting. You are fighting the persons mind using the body as a medium.)