Real Tai Chi is hard to classify, mostly because it's so domain specific. Though I don't talk about it much and I don't practice anymore, I'm a certified instructor in the short form through the William CC Chen lineage (if you're read any of Josh Waitzkin's stuff, that's who he studied Tai Chi under). I've trained with some really high level internal martial artists, true masters in my opinion. Most of them, if I'd pulled guard and done a push sweep they'd have had no defense, and I could have submitted them with ease.
But if I tried to grapple with them like the wrestler in the video, I would get sat on my ass even though at the time I was training a lot of Tai Chi I was a very competitive Judo black belt (and not a small guy either, I fought at 198 lb in Judo and always had to cut). To a man, these guys also punched with incredible power, though their footwork left a lot to be desired (their defense tended to be a lot of rolling and ducking; I thought of them as a bunch of little Joe Fraziers). Their ability to generate power seemingly out of nowhere via minute control of body mechanics was also amazing.
Was it practical? Not very. I think any decent MMA fighter would kick the shit out of them, no question. They certainly weren't used to defending against things like leg kicks or lower body takedowns. But if you played their game, if you engaged in the kind of pseudo-Greco wrestling the guys in the video were doing, they really could do amazing things in terms of manipulating balance and generating power. The power isn't usually striking type power that knocks you out, it was more pushing power or circling power that would spin you off balance. I really did have people send me stumbling 6-7 feet with what looked like a very small shove. We never talked about qi or meridians or any Daoist internal cosmology, the William Chen school is completely non-mystical and all about body mechanics, but some of the results really are amazing. Now, you have to do it for 20 years and you still won't really know how to fight unless you also put on the gloves and spar (which only about half the people did), but when I see people playing the internal martial arts game and getting spun 1080 or bounced up in the air I don't immediately assume it's fake, because I had that done to me. And I'm about as incredulous as it gets, I took up Tai Chi after I left Korean martial arts because I realized that they were just useless air kicking BS. If you play their game, good internal martial artists can make you look really stupid and do some pretty amazing things. I encourage anyone really interested to go to a seminar or find a local guy who's legit. The latter is pretty hard because there is a lot of BS and fraud in internal kung fu, but a good guide to legitimacy is spending a lot of time on push hands and doing at least a little sparring, even if it's infrequent (since the frauds usually don't spar at all and just do the form). Any William Chen lineage school is also a pretty good bet, though there aren't many around outside the east coast and southern Indiana.