Only if you define happiness in your own unique way to make your point a tautology.
If they are content and happy with their lives, and enjoy what they do (inflicting pain), then for all its worth, it is happiness.
If they are content and happy with their lives, and enjoy what they do (inflicting pain), then for all its worth, it is happiness.
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.
There are things that are true because they fit the proper description and there are people who use "No True Scotsman" because they don't want to learn the truth.