Anyway, I have a D tin whistle with a C hole, and the whistle is tuneable. I’ve never retuned it and I’ve never played tunes before that weren’t in D major.
The Altan setting of Dúlamán alternates between the main keys of C Major in the A part, and G minor in the B part. To play along, you should use a C whistle and play in D Major / A minor fingerings.
BTW, that video seems like a thin excuse to rip off the album track. At least this live video from the Cambridge Folk Festival seems a bit more legit.