Many GMs disagree with Kotov's tree of valuations, as it is simply an impractical way of playing. Obviously, you need the calculating ability, but it should be turned only a few times a game.

Instead and this is common to all chess players, most good moves are just immediately obvious. (see Gladwell's Blink, which is true for chess at least).

It has been said, that in a regular chess game, GM might have to have a think 2-3 times a game(see Anand in top form), IM 5 times, an FM 10 times.

As an FM I have to concur with this. When playing a GM, I invariably make a mistake when I start running out of time, as my store of "obvious" moves is much smaller than GMs.

Perhaps I have only 10k positions stored in my RAM, and GM has 100k.

On the other hand when playing say a candidate master, I see them think long and make a mistake, which seems obvious to me immediately.

Still there are players who are more of a calculating type(see Shirov, Kasparov), and some who are less(say Botvinnik, Karpov).

How well does Kotov's book translate to other fields? I've just done very badly at an Android:Netrunner tournament and while I found a lot of deckbuilding issues post-mortem, I also had a lot of mental failings.

The same kind of approach from Kotov can be used on net runner, or more traditional CCGs. You can see how that works in Magic, for instance, where the top players have major amounts of visibility. Someone like Luis Scott Vargas plays plenty of games out there, for people to see, and describing his thought process (which makes him a worse player in those games, but that's to be expected). You can still see the relentlessness that Kotov describes. He knows his options by heart, based on his knowledge of his opponent's deck and all cards available, he makes guesses, dedicates time to each decision, and them moves.

For high level play, there's also issue of deception that do not apply to chess, but will apply to Netrunner. Still, no good player will put deception first in his analysis. If anything, it's the equivalent of Magnus Carlsen's care for giving his opponent as many chances as possible of making a terrible mistake, while still playing very good lines.

Very horribly probably. Though it is a great book, and everyone serious about chess should read it, I think this quote of Anatoly Lein by Jonathan Tisdall in Improve Your Chess Now explains the problem with Kotov best.

"I don't think like a tree - do you think like a tree?"

I believe John Nunn touched on the problems with Kotov's method as well in Secrets of Practical Chess.

The biggest thing to take away from him is the need for a thought process, not necessarily the actual method he describes.

Kotov's method where you calculate every variation only once requires tremendous discipline. Actually, I know no chess player that mastered it. Most hop back and forth between variations.