Pullup Exercise Demo 

I don't see any problem with grip. For strict pullups: Ideally you need a bar a little higher to be able to fully control the eccentric to full extension of elbows and to fully unlock your scapulae in the bottom position. On concentric, explosive pull, ideally to bar below clavicles if you can. Don't crane the neck. You are kipping a bit. I don't mind kipping if that is what is intended with that version of you pullup, but it looks like you are doing a more gymnastic hollow bodied pullup versus an arch back pullup or crossfit kip styled pullup. Give a slight pause at the top with elbows cued down and back, then slower eccentric down. Don't worry about rep count. Keep strict form and rep until form crumbles, then stop and rest.

Your grip technique is very poor