He does answer the question. First of all, this is a simple yes/no question that people would expect you to answer yes to even if you are not happy. There are several instances in the film where this happens to Stephen and this is why he asks Wong the same question.
Doctor Stephen Strange: Yeah. I bet. Truly, I'm just glad that you're happy.
Doctor Christine Palmer: I am. I really, really am.
Doctor Stephen Strange: Good.
Doctor Christine Palmer: Are you?
Doctor Stephen Strange: I'm happy.
So by not directly answering the question Wong is answering with 'No'.
The very next line of the movie after the block you've quoted goes on to confirm this.
Wong: Sometimes, I do wonder... of my other lives. Yet I remain grateful in this one. Even with each tribulations.
Wong considers himself grateful rather than happy.