The link i provided has that as well, and it says that Rawlinson created the short kilt in Inverness, Scotland, with the help of local highlanders. Might have been a guy from Northwest England but he did it in Scotland with the Scots, and it's an apparently dubious claim at that. The sources i provided also suggest that after the invention, the British army popularized the short kilt as opposed to the traditional long one, but it's still of Scottish origin (not developed by the British army as the linked YouTube video suggests. Conflicting claims. I admittedly skimmed through the video to find the relevant part). Still interesting though.

"The design of the small kilt was adopted by the Highland regiment of the British Army, the military kilt then passed into civilian usage and has remained popular ever since"

This does, however, sound similar to claiming that Italy was the first non Scandinavian Western nation to find the new world because Christopher Columbus was from Italy, even though the whole excursion was wholly financed by, backed by, and launched from Spain.

There's also dispute over the claim altogether from Scottish historians.

"Of course, many Scots dispute the notion that an Englishman invented the kilt. Indeed, there is some evidence to suggest that the kilt was in use before Rawlinson’s time. For example, the portrait of Kenneth Sutherland, 3rd Lord Duffus, appears to point to earlier use of the walking kilt. However, there are discrepancies concerning this theory among the Historiographical community, with some experts disagreeing as to the origins of the modern-day kilt.

Michael Fry, an eminent Scottish historian, debunked Lord Dacre’s claims about the kilt saying they ‘prove absolutely nothing’. Fry claims there is evidence that Tartan was worn in the Middle Ages—he also labelled Lord Dacre as ‘not a very reliable guide to Scottish history."

https://www.lochcarron.co.uk/our-journal/the-history-of-the-kilt/#:%7E:text=Originating%20in%20the%20traditional%20dress,cloth%20in%20a%20tartan%20pattern