Humans (roughly) desire to be happy. Imagine aliens who desire to be angry instead.
Isn't it the act of desiring that makes it happiness, not the name?
Only sort of.
While we are happy we have certain mental dispositions which are unrelated to the ones we desire when we desire happiness. Happy people are more likely to give to charity. Happy people (or at least people on certain antidepressants) are also more likely to judge harming others as wrong -- whether this translates into less actual harm, I don't know. Further, people tend to prefer that others be happy -- that's why people are always telling depressed people to smile.
Imagine that in these aliens, happiness worked in terms of its behavioral effects as it does in humans, as did anger. But aliens might still want themselves to be angry even as they want others to be happy.
One of the most important points raised by the sequences is that not all minds are like humans. In quite a few places, people have discussed minds with slight changes from human minds, which seem altogether different. However, a lot of this discussion has been related to AI, as opposed to minds created by evolution. I'm trying to think of ways that minds which evolved, and are effective enough to start a civilization, could differ from humans'.
Three Worlds Collide would seem like an excellent starting point, but isn't actually very useful. As far as I recall, the Babyeaters might have learned their baby eating habits as a result of societal pressure. The main difference in their society seemed to be the assumption that people who disagreed with you were simply mistaken: this contrasts to humans' tendency to form rival groups, and assume everyone in the rival groups is evil. The Super-Happies had self modified, and so don't provide an example of an evolved mind.
So here are my ideas so far.