I'd guess he just eq'd and compressed the life out of the kick, and added some nasty chorus to the hats, but what you see in the video is not what it appears - the empty kick stand, and no mic on the snare - just that mid field one? The missing cymbal suggests it was made pretty for the camera.
My guess is he miked the sources separately so he could leave the side stick clean, process the kick and have enough hats to do the weird swimmy chorus.
I guess I'm just not a lover of over-treated drums. This ones sounds better on my macbook speakers than in the studio where the noisy drum treatment annoys me. I don't really hear over level distortion on the kick - just the sound of a compressor squashing the ransient with a quick release. It might be distorting, but it's so quick it is difficult to tell. I suspect that maybe the mic on the boom did the side stick - but as this is treated differently to the hats, the hats were perhaps recorded on a different pass? There's lots of annoying noise though - it makes the loop very evident when it goes quiet for a fraction of a second.