Interesting mix of traditional, close embrace milonga and more modern elements in open.
Samina, this is milonga, so it's different from tango. It's not particularly fast for a milonga - though of course you'd need to be a great dancer to lead and follow a lot of these steps. For social dancing the moves would usually be a bit more subtle, but the dance could be just as fast.
As Twirly said, that's milonga. It's one of the 3 variations of AT.
You know when I said I could recommend a couple of good teachers in NY? These are them. He's very sweet, and funny as hell. (The last time I saw him, he ended up pantomiming (sp?) being shoved in a cat carrier. I was laughing so hard I was crying.) I don't know her well, but she's sweet and just...so...cute and tiny! (I'm 5'3". He's the one I'm dancing with in my avatar, and I had on 2.5 heels, so he's what, 5'5"? If you look at the video, she's shorter than him by a decent bit, and she dances in 4" heels. Tiny!)
One thing I love about the two of them dancing, is that their faces show everything. It can't be seen very well on the video--although there are a couple of quick spots--but when you see them live you can see just how much the love dancing, each other, and dancing together.