Not a parent, but this thread caught my eye as I did the exact same thing when I was younger.
Your son might just be doing it because it feels nice (in which case, don't worry, just make sure he washes his hands regularly), but my bet is that he's doing it for the same reason I did it, and for the reason he says he's doing it: his hands/feet are dry and his eyes itch.
I still suffer from chronic dry skin, but when I was little I had no idea what it was or how to deal with it, I just knew that my hands were dry and they felt weird and I needed to get them wet. Somehow spit was more comforting, I think because it was more gooey and it took longer to dry. I also used to rub my eyes like crazy until I had to train myself out of it (makeup...).
I recommend lotion and eye drops
If he doesn't like eye drops (I know I sure didn't), then I'd talk to his eye doctor. I'm no expert, so maybe there's something else that can be done for chronic dry eye.
If it's not that, then he's probably just rubbing his eyes because it feels good (I'll admit I still do this sometimes, after my makeup's washed off and my contacts are out, of course). If that's the reason, I wouldn't worry, he'll more than likely be fine. I beat the heck out of my eyes when I was a kid and nothing bad ever came of it, at least...