What exactly does "solved" mean? I'm assuming it means knowing the correct response for every move your opponent makes, i.e. those which always lead to a win? How does that work if your opponent is also making the correct response for every move you make? There can't be a path that results in both winning, though maybe a draw - is that "solved" then? What if your opponent makes a move that has no winnable solution for you? I can only realistically see it as solved if both players are in collusion to bring about a win for someone - and at that point you're not playing a game, but collaboratively solving a problem.

Taking a really simple example: noughts and crosses / tic-tac-toe is "solved", but generally leads to a draw once people know the process. You can only win if someone doesn't know the methodology, makes a mistake, or deliberately doesn't do the correct move. However, the paths are very, very limited unlike for chess. According to Wikipedia, we're talking 765 combinations of positions that can be solved by just 8 rules. As long as you have two unassisted humans playing, there's no way for the solution to every possible move in chess to be handled.

Edit: so, in summary, yes people will continue to play it. :-)

I think casuals will still play it, but it won't be taken as seriously anymore at the higher levels *assuming* that GMs can actually implement the correct series of moves. So if GMs like Nakamura or Napomniatchi can implement perfect play, then I think chess will die out as a competitive sport.

However, if chess is solved but can only be played perfectly by a computer from all positions (presumably because no human can memorize all the correct plays), then it won't really affect anything. Such an outcome would be indistinguishable from the current state of chess, which theoretically does have ideal moves, its just no one knows what they are. We already use stockfish as a pseudo-objective guide as to what moves are ideal, so the only difference is we would have a perfect chess engine to compare our mortal brains to.

It would definitely change chess strategies though, as Anand has pointed out with respect to AlphaZero.