Well, it's clearly not a reel.

It's mainly in 6/8, so more like a jig, but it doesn't really sound like a jig, melodically, to my ears. Rhythmically, the opening few bars are heavily syncopated, and this extremely rare in Irish music.

Of course, someone else might come along and say, 'Oh yes, that's called The Old Man's Plums', or something, but I'd be very surprised.