Great vid! I can sort of explain some of the tricks though. Provided you're playing in the right time signature, most drum beats will fit a track. You can see Chad work out that the track is in 3/4 (or 3s as he says) pretty early on. He gets the accents on the snare pretty quickly too but the give away there is that the bass line will hit those same accents so you can hear where the crescendo in each bar will be in the bass notes when the drums are removed.
He does an awesome job of judging the ebbs and flows of the track from verse-to-chorus-to-bridge etc. and he switches gears really well in a way that makes it seem seamless. But really what he's doing is swapping which cymbal he's holding the rhythm on. The beat remains broadly the same which gives him room to correct the volume if he's missed the transition. He plays the ride cymbal in the chorus which gives a bigger, more treble-filled sound, then switches to the hi-hats for the verse which sounds sparser and allows the little details (like the paradiddle at 2.10) to cut through. If he missed the change and the chorus continues, he could open the hi-hats and keep the sound large without skipping more than a beat.
Most gigging drummers will be good at this because often your on-stage monitors (the speakers or earphones you hear the rest of the band through) can be error-prone so correcting errors in those transitions when you miss them becomes second nature. It's the same reason drummers can cue transitions in jams at open mic nights or in jazz ensembles. It's kind of like a rip cord that allows you an 'out' even when you pass the apparent point of no return.
You can see at 3.41 where he expects the track to switch back to the chorus or a treble-heavy middle 8 but it actually drops into a bridge. He starts the bar on the ride cymbal and transitions to the floor tom half way through the bar when he spots the error.
All of that said, and even with the tricks being identifiable to the trained eye, he pulls them off incredibly well and drops straight into a difficult and well-rounded beat with fills and accents galore with incredible ease. I certainly couldn't do anything like as good a job as that.
I think you'd see drummers trip up a lot more on tracks where the time signature changes so, while this is no easy track to drop into - being that it's in 3/4 (6/8) and not a classic 4/4, something like Rush's Tom Sawyer would be much harder to manage this with. Even some seemingly simple pop tracks switch from 3s and 6s into 4s and back. The Beatles' Lucy in the Sky with Diamonds is the obvious example but more recent tracks like Hozier's Take Me to Church do it too.