It's a traditional grip, more later. A lot of drummers use matched grip, which is just as it says on the tin - both sticks are held the same way - as in this drummer's right hand. A lot of drummers, jazzers included, use a traditional grip, though. Sometimes called cross grip, amongst others.
The traditional grip then gets split into three styles.
French grip, with the thumb on the top of the stick.
German grip, where the thumb is on the side, making the palm face upwards.
American grip, which is sort of a half-way point between French and German.
In the video, the drummer's thumb is well on top,but he rotates his hand a lot, making it the American grip.Its history is probably from the marching side drum, where it was easier to play using that grip than any other, due to the positioning of the snare (side) drum more at the side of the body (hence the name) rather than between the thighs as is general in a standard drumkit these days.