He's playing in the key of C on a F-Bb-Eb accordion.
He's hitting a whole lot of bluesy notes!
You are correct that transposing the song to your G-C-F accordion would use the same fingering.
Do you play a single row diatonic? If so, one of the ways to get started on a triple row is to play it as though it was single row and then start adding notes from the other rows.
Since the song is in C, much of the song is played on the outer row, which is F. This means that when he is on the outer row, it is the same as the "pull" or 2nd position, on a single row. If you played the C scale on the outer row, it is actually the C mixolydian mode as the 7th degree of the scale is flat - a half step lower than C major.
(In your case, it would be D mixolydian on the outer G row)
I haven't tried this, but it is probably possible to play much of the song staying on the outer row. Switching parts to the middle row gives almost all the same notes, but the fingering is easier for certain runs. You do pick up one very useful note on the middle row, which the flat 3rd of C (or D for you). I cannot understate the importance of finding and using that note - it is worth the price of admission to the triple row.
I don't know how much more I can help. If you haven't played a triple row or even a single row at all before, you've got a lot of work ahead of you.