Interesting point. Yeah, I think that occurred to me at one point, too. I've come up with a couple possible explanations.
First off, the Chee are more than just their programming. They're sentient creatures too, you know? They are not rigidly bound (well, except for the nonviolence thing) to do as they were programmed to do. And so I think, maybe they were once playful and happy beings. But the extinction of their masters surely had an effect on them. I know I'd have a hard time being playful and happy all the time, if I'd witnessed death on that scale. Plus, as Erek points out, the Chee's memories don't wear out with time the way living creatures' memories do. So they remember that massacre just as though it had just happened. Heck, if I were them, I'd be downright depressed, all the time. It's a testament to their optimistic personas that they're able to function on any social level at all.
The other thing I noticed, was that it says in book 10 that they do play, with dogs and each other, in their little basement-dog-park place. At least, I think that book mentioned some of them chasing each other around.
I imagine that the Chee probably prefer each other's company to that of humans. After all, they're basically immortal, whereas humans grow old and die. They probably tried to avoid getting too close to humans if they could avoid it, just to minimize on the pain of seeing a close friend die. Erek's relationship with the Animorphs was pretty much purely professional, and necessary because he didn't want earth to fall to the Yeerks. But he'd have no reason to want to play with them. And since the books were told from the Animorph point of view, it stands to reason that they don't tend to see any of the Chee playing very often.