Messages.app (Mac) does not play sound when message received
I had the same problem and I found that in System Preferences> Sound> Sound Effects: The "Alert volume" was set at zero. Adjusting it up solved my problem.
I had the same problem, I think I found what it was, for me at least.
System Preferences -> Sound Effects -> Play sound effects through: Internal Speakers
My issue was a software program that somehow became my default sound program. I changed it back to internal speakers, and all is well.