Is this normal behaviour for an 8 month old kitten?

I have just adopted him - we do not know much about his past except that he was on the streets for at least a few weeks before he was rescued. He is a confident, easy going little guy who purred and snuggled into me the first time I picked him up. I have had him 5 days and he just loves affection and is very friendly. However 4 times now he has, for no apparent reason, entered a room where I was with wide eyes and tail lashing, launched himself at my arm or leg, clung on and started biting me. He digs his claws in slightly but does not do that or the biting hard enough to hurt much - it does hurt a bit and leave small marks. I am not sure if he is playing? He does not hiss or arch. Before he came in and did this he has not been upset. I have, on each occasion, detached him saying 'no!' and walked away to show that this is not a way to get my attention. Is this just kitten play?