I'll present an independent view on this, even if some of the Top Dogs in here might bite
The misunderstanding between both parties (the theoretical and the mental
) might just be based on this:
The tennis/sports example is way oversimplified and thus misses the point.
You do not just magically, "instantly" know what you want to do.
I would rather describe the process as
1. perception (might slightly be altered by mindset)
2. mental execution (critically depending on mindset)
3. physical execution (mostly depending on physical skill, but mindset can have influence)
Here, "mindset" refers to everything going on in your mind, which might be a lot (if your girlfriend just left you) or just the right things if you are in a state of flow.
Now, for
tennis, we have the following:
1. you perceive the ball+opponent (unless distracted by external/internal influences)
2. you "plan" what to do. For sport this quick, this basically just means pattern recognition and instantly reacting to what you see. Still, the mindset comes into play here. Just because it happens very fast, does not mean that it is a fixed, automatic process. It obviously depends on mindset. You might e.g. pre-decide to play aggressively or defensively, hit on his backhand most of the time, etc.
If your mindset is not good, you are prone to errors here. To be a top player you obviously need a top notch planning network here, the functioning of which obviously depends on your state of mind.
3. You execute. How good you do it mostly depends on your physical condition, skill and training. Still, your mind might be so far off optimal that it interferes with the body in some way at this stage.
Now, for
poker (and chess etc.), the process is exactly the same, the only difference being that phase 3 is almost completely trivial.
1. You perceive situation and opponents (might already be altered by mindset)
2. You mentally execute, planning what the best move is. Mindset plays exactly the same role as in tennis, probably a little more, because you can think much longer about it.
3. You toss chips/cards looking detached
So in conclusion, the mental game and state of mind are equally important in poker, chess, tennis and golf. And they clearly are the key success. The slight difference is just the fact that in tennis and golf, the mind also plays a role during actual physical execution.
For some background: semi-pro poker player. I have no (mental) coaching experience whatsoever, I just play all the 4 games mentioned and every other time my mind plays tricks on me. I liked Tendler's book.