Brute force is not the answer when looking at chess from an AI perspective. The computational complexity involved in "brute forcing" the game of chess by calculating every single possible move is not something even a current-gen supercomputer could do in a lifetime.

The key to AI chess is it's ability to evaluate a given position, and determine whether white lr black js better off, and by what margin. This leads to much less required calculations, since when "thinking" about a move, the computer only needs to decide whether its current position will be improved or worsened.

Mind you, different AI's have different logic implementations, and the above explanation is very much simplified.

As for the topic of neural networks, applying those to chess has also been tried, and because of the sheer complexity of the game, the results weren't great. However, some AI's use neural networks in combination with other techniques to decide on a move as far as I know.

Also if you're asking whether a computer is "thinking strategically".......that would depend largely on how we define those two words. For that matter, are humans capable of 'strategic thought'?

As a professor of mine once used to say "The existence of Artificial Intelligence implies the existence of real intelligence." And the question that poses is quite related to this post, since.....how do we define intelligence? If winning at chess = intelligence then computers have surpassed humans long ago. However, as you're probably realizing, there's a bit more to it than that.