That's a "no true scotchman".

Happiness is simply being happy (or, if you want, content and enjoying yourself).

If you do that by inflicting unhappiness, or by depriving others of things, etc, it's still happiness.

There's no part of the happiness definition that says it's incompatible to with "unhappiness to result in others". That might be part of Bhudism or Christianity etc, but it's not some given of human nature.