Chess is quite tactical and brute-force-y -- the board is quite small, games are quite short, and there aren't all that many possible moves at any given point.
A program can play pretty good chess on modern hardware just by alpha-beta searching with a fairly simple evaluation function for the leaves of the search tree.
The best programs are cleverer than that; they have sophisticated evaluation functions, they prune and extend their searches, etc. But at heart, what makes them so strong is that they can search deeply.
That approach doesn't work so well for go. The board is 6x the size, games are 4x as long, the "branching factor" (number of moves available in a given position) is 10x as large. (All figures very crudely approximate.) If you try to make a fairly-dumb searcher in go, it will play very badly.
So how do humans manage to play well in go? By smarter searching, with a better idea of what moves are worth considering; by thinking strategically; by having a feel for the shape of a position ("moving here is likely to be very valuable").
Those are all things that feel like they are harder to make a computer do, and come closer to actual intelligence, than doing well at chess just by doing an enormous search.
The first of those is certainly correct. AlphaGo (like most modern go programs) organizes its searches in quite a different way from a typical chess program. It's not clear how far it deserves to be called smarter, though, since a lot of what it's doing is playing out lots of games fairly stupidly[1] and seeing how they go on average.
[1] Compared with how it actually plays. One of the achievements of AlphaGo, I think, is that it can reasonably quickly select moves for its playouts that are actually pretty good.
The second is more debatable. But, e.g., AlphaGo selects and evaluates moves using neural networks trained on a large amount of high-quality play, and the effect of this is that given a position it can quickly "see" how good it thinks the position is and what moves might be effective, without doing any searching, as a result of feeding the position through a big neural network that does some mysterious calculation we don't understand well. Which is, at that level of abstraction, pretty similar to what you might say about a human go player.
Whether any of this has any bearing on more general artificial intelligence is an entirely different question, which I will not attempt to get into.