"The game server did not receive a response from the Steam authentication servers."

This means the server was trying to log you in, but wasn't able to verify your Steam account within a reasonable amount of time. (default 15 seconds)

Unfortunately there is nothing you can do about it except try again later. It might be a one-off issue, or it might persist for a couple hours.

Explanation

When you join multiplayer the server has to check with Steam that "you are who you say you are" so to speak. Basically your client tells the server your Steam ID, and then the server asks the Steam backend whether that's correct. Otherwise cheaters could impersonate players by using the Steam ID of another account.

Usually it happens when the game server has temporarily lost connection to Steam. Especially on Tuesdays when Valve performs Steam's weekly maintenance.

There is nothing the server host can do about this unless it has been happening for a long time (say, 8+ hours) in which case there might be a problem with the server's network configuration / firewalls.

Behind the scenes

This means BeginAuthSession returned k_EBeginAuthSessionResultOK but the ValidateAuthTicketResponse_t callback was not received.