The sound sample didn't seem to be accessible any longer, but I did find somebody's transcription of the Brady arrangement, as The Ride in the Creel, at  http://www.ismargad.com/Creel.html

Not having heard the recording (so far as I remember), I couldn't say how accurate it might be; it looks reasonable enough. From the wording, I'd guess it to be an Ulster form of the song, but could easily be wrong. Brady seems just to have described it as "trad arr", for which laziness I've always felt professional performers ought to be strangled.