Yep - it's playing!
We got a kitten about 12 months ago. Within a week of her settling in she became totally wild - but not in a malicious way - just excess energy! We were unable to walk past her without her wrapping her front paws around (into) our ankles and biting our legs. Every time she was picked up she'd bite our fingers. We took a risk and got a second kitten - they spent (still spend) lots of time chasing each other and play-fighting, and they're both really calm and soppy towards us
A couple of days ago we found a tiny kitten on the highway. She's exactly the same - full of beans.....and teeth....and claws, lol!
Sadly DH won't let me try the same solution again