No, we are not all striving to have more happiness (although some people surely are). So long as you don't circularly define happiness as "that feeling you get when you accomplish your goals", then most people have at least some goals besides happiness, and some of us explicitly advocate that many or most goals should not be happiness related.
Also, I failed to mention why I replied to the parent post: the mention of moderation. I think if you are listening to how you're feeling, you can (one can) tell when a life strategy isn't working. The important things in life will make their demands known.
In the past year, I've racked up more than 400 hours playing RimWorld, well over two weeks just playing that. I'm sure I could have found something more useful and interesting to do than that.
Personally I think spending time playing games, reading, watching tv and other activities are essential to remaining productive. Not least because they are all interesting input to consider things in different ways. But also because they give me space.
As with most things, the key is moderation: finding a balance where you're getting enough relaxation/leisure to keep yourself happy, while not dedicating so much time to it that it completely takes over your life.