That's the one! My grandfather is a Methodist preacher, so I grew up with these hymns. It's fascinating; I'm just now learning how many of them came from Wales.

I'll add that the version they're singing is to the hymn Love Divine, All Loves Excelling. Another common hymn with the same tune is Come, Thou Long-Expected Jesus. The most common accompaniment to Love Divine All Loves Excelling is Blaenwern, which also happens to be Welsh!