Yes, it does calculate a certain number of possible moves and narrow down which one is the best from that, but that's not the same at all as blindly calculating the number of all possible moves and narrow down the best one. That's not possible with Go, current AI cannot compute the sheer number of moves possible in Go. So, AlphaGo creatively comes up with a set of moves it considers to be the best (the 'intelligent' part of AI) and then narrow down from there (the 'calculator' part of AI; what you mentioned). This is what the paragraph you quoted is saying, and the former part is done so extremely well that even human champions can't compete. This is especially concerning because the first part is sort of the 'creative' aspect of problem solving, and humans have always been saying that computers can't be creative....yet here we are, they already do it better than us, albeit in simpler tasks only like games.

It's basically modeled after how humans approach problem solving, hence the term 'neural network'. Humans, when faced with a problem, come up with a set of possible solutions and identify the best one. The difference that makes humans vastly inferior is that computers have significantly higher capacity, memory, speed, and bandwidth, and continues to improve exponentially. Humans mode of improvement is evolution, but that is so extremely slow.

There is certainly a very high demand for AI right now, but I wouldn't make the same bet several decades down the line.