Odd wording since it could mean that neutral cities become happy or that you could ignore the mood drop. I'd assume it was the latter - I'll check on my French version, if you don't get another response.
You can take my game… when you pry my cold, dead fingers off the board!
That's pretty much it, but it's a little more nuanced. I think the reason we just didn't say his city is immune is that it left the question open of whether any of your other cities had to be affected. So you are essentially immune as long as his city is the one that can be affected.
For something like Famine, it also doesn't exempt you from losing Food... it just protects you if you have no Food and have to drop mood.
It's also optional, so if you want to lose units to Black Death for VP, or turn some cities angry for an objective or something, you may.