I had always thought the deep bass note is the driving force behind the song. Much like the low rumbling and deep bass sounds indicate foreboding and fear in a cinema experience.  Relentless with a hint of dread.

But then again, the chord progession is rather haunting and Annie Lennox’s vocals (top-notch) are stark and beautiful.  Maybe it’s the syncopation?

From the description (arranged for order):

I’m going with the 8-bit or the dual piano (2 and/or 4).

‘Piano version, 8 bit version, ragtime version, dual piano version or the terror version…’

The original video is mildly surrealistic 80’s shock-pop; just cheesy enough to flirt with schlock, but the combination of lyrics, story, musicality and simplicity give this song serious staying-power: