I don't know much about HEMA, but why would you have a guard that requires you to hold the blade?

I can understand it on a single-edged blade but on a double-edged sword?

Fascinating... the attacks and parries are pretty sophisticated...

I don't know, but I've seen it before in other demonstrations or illustrations so they must have had good gloves . I figure that the blade was probably only kept sharp at the tip.

from wiki on the ineffectiveness of cutting slashes against full plate:
"To overcome this problem, swords began to be used primarily for thrusting. The weapon was used in the half-sword, with one or both hands on the blade. This increased the accuracy and strength of thrusts and provided more leverage for Ringen am Schwert or "wrestling at/with the sword". This technique combines the use of the sword with wrestling, providing opportunities to trip, disarm, break, or throw an opponent and place them in a less offensively and defensively capable position. During half-swording, the entirety of the sword works as a weapon, including the pommel and crossguard. One example how a sword can be used this way is to thrust the tip of the crossguard at the opponent's head right after parrying a stroke. Another technique would be the Mordstreich (lit. "murder stroke"), where the weapon is held by the blade (hilt, pommel and crossguard serving as an improvised hammer head) and swung, taking advantage of the balance being close to the hilt to increase the concussive effect."

@drradon -- It was cool to compare this with the limited stuff I can remember from taking an intro to fencing (foil) class in college.

There was a different parry for incoming attacks to each quarter of your body facing the opponent (top-left, top-right, bottom-left, bottom-right). And that's just for 2 opponents both using the same general stance and weapon. I'd guess these guys would have different counters for each combination of stance/style, weapon of their opponent, and target area. That's a lot to remember -- although a lot would be relatively consistent across different combos.

I liked the high guard styles (two named "guard of the lady" stood out), because they seemed to pair nicely with "beat attacks" -- where you attack and swing to hit the opponent's weapon rather than their body. Gets their weapon out of position and leaves you in better position to make a second attack that they can't easily parry.

I wasn't very good at fencing. Bad footwork, not good form, and pretty slow on parries. But the one thing that let me win matches was aggression and beat attacks. The instructors and more skilled people could see it coming and dodge or otherwise counter it (especially after they figured out that was the one reliable tool in my box), but it was a fun technique to use for me. Cool to see these guys do pretty much the same thing, but just as a small part of a much bigger bag of tricks than I had.

This is, in fact, rather common. If you take a look at fencing manuals (Talhofer and the like). Please remember that the blade was not razor-sharp because it was supposed to work against mail and plate.