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Is the Monte Carlo approach specific to Go in terms of A.I. challenges? Or is the Monte Carlo approach gaining traction in other A.I. problems as well?

I am tremendously unfamiliar with recent A.I developments.

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Monte Carlo Tree Search is a key technique in previous computer Go programs (and other games). The improvement here was using the deep learning network as the value function to evaluate nodes in the tree and the policy network to determine the search order.

MC tree search isn't specific to Go, no. It's been used for other games including imperfect information ones like poker. I believe that the main reasons for using MC search is that it does not require an evaluation function, and it acts as an anytime algorithm so you can get a "good enough" answer within arbitrary time constraints.

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