I'm not sure if this works in the version Kent used, but the way I found to easily select islands is to use FACE mode rather than VERTEX mode. Then you can use L to select an island. I know this has been working in several versions that I've tried going back to at least the 4.x series.
I personally use island select mode( the 4 at the top of the keyboard. Not numpad) in the UV editor.
Note: I haven't watched this yet
That works for UV editing, but this video was more mesh modeling setting up physics sim :D He was in Vertex mode, which if you L to select linked, you select everything. I think Edges also does. But FACES will make it easy to select the island groups that are connected by edges.