Is Chess Doomed by Artificial Intelligence?

That's more than a little like asking "Is Trivial Pursuit doomed by Google?" If the objective for playing chess is to beat a computer, sure. If not, it's game play as usual. The computer might be able to teach you how to play better, but doom is an unlikely result unless AI finds a never-fails solution to the game, like was easily found (by humans) for Tic Tac Toe.