It's a tune called Durang's Hornpipe, which American dancer John Durang used to dance to:
https://tunearch.org/wiki/Annotation:Du ... ornpipe_(1)
Durang was a supposedly favorite of George Washington's, and credited as the first famous American dancer. The hornpipe was his signature dance, and it looks like he wrote this particular hornpipe himself:
https://upload.wikimedia.org/wikipedia/ ... Ditson.pngThe dancer in the video you posted is Wayne Sleep, a well-known British dancer who trained in ballet, and between that and the video being a sort of historical reconstruction of an American dancer from the 18th century, it's not going to look like dancing an Irish hornpipe at all!