I really do NOT think he is doing this on purpose.... and he is still young. Sure, he's been potty trained. But that has nothing to do with it.
My girl, is now 7 year old. When she was in Preschool and Kindergarten and 1st Grade... she and other kids had accidents. I"m not talking a little squirt of a leak on the underwear. I'm talking real pee accidents. The Teachers said, this is normal. Normal.
Next, there are many kids, adults included... that when they laugh or if they are horsing around or having fun... a little pee leaks out. Not because they did it on purpose. It just leaks out INVOLUNTARILY.
You said yourself, that the wetness on his underwear is only "damp"... but not enough where other people/the Teacher can tell. Right? So, its not a full-blown pee 'accident.' It is pee seepage or pee dribbling or leaking out, a bit. It is NOT like he is emptying his entire bladder and then creating a huge puddle of pee on the floor beneath him. Right?
SO, this is a BIG difference.... because he is NOT peeing a puddle on the ground... his is a "leaking" of a SMALL amount of pee, onto his underwear.
Next, MANY kids, do that. MY daughter included. And she is 7. Or, whenever her bladder is real full and she goes to the bathroom, a tad little pee may escape out. But it is NOT her doing it willfully... it is just a leak. A SMALL leak. Not anything to punish her about... because it is involuntary. INvoluntary. I know she is NOT doing it on purpose... and besides, why would a child continue to leak pee on purpose... if it only brought them punishment and nagging and lectures and scolding by the parent???? NO child would do that on purpose.
Your son's situation, to me... is not him doing it on purpose. Nor consciously. I think, that when he is awake and active (as most kids and boys are), and when he laughs or what not, a little pee just leaks out. NO biggie.
all the best,