IMHO the swords you have been discussing are all from c. 1500 AD more or less. Do they also use earlier swords, such as the Roman Gladius and Gaullic Long Swords. Or Axes, such as the Frankish francisca.
Good observation. The longsword techniques come from mostly 13th to 15th century "fechtbuchs" (fighting books) in german. The single-hand sword and shield or sword and buckler has some works a little earlier. It's not assumed that the Germans were the only masters but they along with the Italians seemed to be among the very few to write anything down and preserve it.
The archaeology of swords gets dicey because steel just doesn't survive well. There's more bronze-age swords surviving in museums in better condition than far later steel swords.
The Viking sword I pictured was a common design in use for a very long time, beginning in the 8th century all the way to the 11th or so, at which point the distinctions between the Norse design and the European single-hand start to blur, as might naturally be the case.
Before that, there is precious little written material to work with. We don't know with any certainty how the vikings used their sword and shield or if it was different from how the other later European writers put it down. It's probably reasonable to assume that there were many commonalities. Body mechanics and physics dictate what works well, so it is probable that most sword and shield, and longsword technique was similar.
We do have a growing curriculum on pole arms: spears, halberds, pole axes... that sort of thing. Those things of course go way back into lost time. The staff and the spear have been with us since Man first picked up a stick and sharpened it.
I'm hoping to get into axes, especially the Viking axe, but I've got a long way to go with what I've already got.
It's been said that the "dark ages" weren't dark, they merely went unrecorded. They're called dark because there's just not much detail surviving in the written histories, not because there wasn't anything happening. Sadly the same is true of any detailed treatise on fighting arts. What we know is gleaned from paintings, stories and legends, but it is light on detail.
With regard to the Roman gladius... interesting question. I don't know if anyone is developing a curriculum for that or not. There is probably enough material surviving to reproduce a fair fighting manual. But I don't know.
The organization I'm in does focus mostly on the medieval and renaissance period in Europe. Partly it is to rediscover and preserve an important western cultural legacy that has been lost or ignored for too long. Partly too, I suppose it's because that's where the available material starts. We'd love it if we had a fighting manual from 5th or 6th century Saxons or Normans... but they along with everybody else wrote down precious little. The fighting arts certainly existed, but were passed down from teacher to student; Captain to soldier, generation after generation and nobody thought to videotape it. Dang it. :-)