You're right, there is no living tradition and all of those techniques are recreated from medieval texts, known as fechtbuch. You could call this experimental archeology. The only living sword traditions in Europe I know of are of classical fencing, which is the more martial cousin of sports fencing.
Any sword style which has two hands on the weapon would have similarities. There are different biases, but still a lot in common.
Arnisador: I have to say that I don't think they're going as fast as they could. Even I can go faster and I'm a lot smaller, weaker and inexperienced. Afterall that is a demonstration about techniques. Although if I had to go faster, I would like to wear a fencing mask for safety's sake.