First one could be a dolly or even a steady cam. All the rest it was a steadycam.
Why it didn't float? Floating is a side-effect of cheap steadycams. It shouldn't float. And it doesn't on this video. But, on some shots, another side effect of steadycams was visible, the horizon twitched a bit sometimes. Balancing a steadycam rig is not easy, but I could see that it was a good steadycam op.
All of them had a focus puller, but the first shot wasn't really good on that area, that's why we all noticed and thought it only had one on that shot. But if you set your eyes on the background and foreground on each shot, you'll see that the out-of-focus changes a lot and not just because the camera is moving away from them. The guy walking also doesn't walk at a constant speed, hence the need for a focus puller. Probably with a whip.
The internet nowadays is full of filmmakers that learn on their own, or want to be the next big thing without actually working their way up, or maybe they just take it as a hobby. As a result, there are a lot of videos and products for filmmaking that aren't good. There are S___loads of cheap "steadycams" that give you that "floating" effect, and a lot of people reviewing them saying they are awesome, and a lot of other people that "learn" from them. I've seen a lot of these videos and none tell you that steadycam ops not only have good gear, there is a technique involved, how you walk, how you handle yourself, has a lot of impact on how much the footage will be stabilized.
On the camera side, I'd say it was with a 7D and a 24mm for most of it, judging from depth of fields and background blurs.
Hope it helps. I do this for a living (DP for small/medium things and focus puller for medium/big), so any question I'll try to answer it.