Interesting song pick, Sharke. Definitely get ones attention.
My $.02, I go with Yorolpal in this. Performance is simple. Lead vocal track, backup vocals, hand-claps, piano player (playing bass and chords). I think the lead vocalist just went with it, and might have a poor sense of song structure/timing(?). The piano player just followed behind (or played catchup) in some spots. The handclaps are not an issue because they just follow the steady beat. The backup singers aren't an issue. They also come in based on the lead vocal line. Everything is keyed off the lead vocalist. I wouldn't doubt if this was a one-shot recording. It worked well enough, so they kept it.
And as the link Jamesg1213 posted, this shows a more recent performance and it is straightforward with the timing.
I do like the song (odd timing and all).