Since we don’t have a Chiff & Fipple Traditional Piano & Comic Dance forum, I figured I might as well ask here in hopes of netting an answer from the broadest group.
So I came across this lovely hornpipe and am wondering by what title(s) it goes by.
Thanks!
Wow how strange.
The tune does sound like it could be a traditional hornpipe but it doesn’t ring a bell.
Well I guess that dancing is no more strange than the Sailors Hornpipe as done by Scottish Highland dancers.
It’s a tune called Durang’s Hornpipe, which American dancer John Durang used to dance to:
https://tunearch.org/wiki/Annotation:Durang%27s_Hornpipe_(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/commons/4/42/Hornpipe_Ditson.png
The 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!
One of those tunes that found its way to Sliabh Luachra and started a new life there, as a reel. 
Though called a hornpipe, it’s a reel here too