I've seen this message several times before when I open Play, after which I am still typically able to start a game with no issues. I've never had it in the middle of a game, though.
The chess.com server was having some issues last night (thread about it here), where people could not start games. A message would pop up saying you've been disconnected from the server, and then when you try to start a game, it would say "matchmaking failed." Maybe this issue is related to the one you're having today.
I keep getting this message while playing. I'm thinking maybe it's a server overload. My internet connection is completely fine, so not sure what else it could be. Let me know what you think!