I think the first thing to note here is that the drum track you're hearing on this is most likely a sample. The sounds have a fairly distinctive quality that comes from being sped up from around 120bpm to around 160bpm (about a 33% increase in speed).
Recreating this is not impossible but, as this is a sample, you will need to think a little like a real drummer.
I attempted to rebuild this quickly using Garage Band. Here's the basic pattern:
You can see that the high hats are falling on every 16th note except for the last 8th which carries an open high hat. The kick is falling on beats 1 and 3 1/2 - this half-beat offset is what gives it that little jumping feeling halfway through the bar: you expect the beat on the 3 but it doesn't arrive until half a beat later.
The snare is more complex with the usual hits on 2 and 4 but with a couple of 'ghost' hits at 2 3/4 and 3 1/4 - these bring in that skipping feeling.
For some extra depth, I played with the velocities. The high hat alternates between 80 and 40 which sounded right with the drum sounds I was using. The point is to offer a little texture by simulating the difference between the drummer's right and left hands.
Similarly, with the snare, the regular hits have a velocity of 80 and the ghost hits are much lower at around 20. Again, this simulates the drummer dragging the stick onto the drum with their left hand.
These velocity settings sounded right for the sound I was using but may be different for you, so don't be afraid to play around with them.
And lastly, don't forget to tweak your sounds by pitching them up a little if possible - this will give them a similar feel to the sample used in the original track.