I've read it now, and I don't think there's much I can add to the erudite commentary already posted.
I really wanted to like Chess - I was in the chess team at school (and my brother actually represented our country in the game), and I later used a chess manual similar to that described in the story to improve my game and finally start consistently beating the brother of a friend who until then had regularly wiped the floor with me. So I definitely had a connection to the story. The problem for me was the way it shifted from Czentovic, whose story was a fascinating one that could have really gone somewhere, and turned him into an unpleasant and greedy opportunist with no further development (apart, perhaps, for his brinkmanship at the end). At the same time I lost a lot of sympathy for Dr. B because of his contempt for the ordinary man, so I had a hard time identifying with anyone in the story. I found it somewhat depressing in that respect, and can see potential foreshadowing of his suicide in the ultimate negativity of the tale.
I also struggled with the idea of someone being able to play chess with himself in his mind, though I laud Zweig's plot contrivance - an interesting concept that didn't quite convince me.
All in all, I'm happy to have read it, and read the discussion, but it hasn't prompted me to read any more of his works.