I took Tai Chi during college from a guy with a passion for it (his day job was as a sign painter and he was a pretty firm Christian), with no mystical overtones to his interest at all. The one thing he drove home, repeatedly, was that if you wanted to be prepared a case where you needed fight, there were self-defense classes available, and to study that. He'd even help you find one.

While some of the things he described about studying with masters had elements of the video you describe (if put less strongly), he also expressed that this was folks who had been studying for a long, long time, and moved on from the rote movements associated with Tai Chi to other aspects. He said he'd been studying awhile (at least ten years) and didn't think he could use it to defend himself.