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Strange question, how energy efficient is this? What exactly is the battery doing and how much energy does it take to do it?

Energy efficiency is not very high, there is quite a bit of friction.

The battery powers a short section of the coil, the magnets do double duty, they're commutators carrying the current from the battery to the coil and provide the static magnetic field that is one half of the field causing the forward movement, the other half is provided by the magnetic field induced by the current through the coil.

The coil being wound one way (right hand) or the other (left hand) coupled with the direction the magnets are pointed in determines whether it is going forward or backward. If you turned the 'carriage' around it would go the other way.

Elegant.

I prefer this video[0] where they go through different iterations to try and improve the speed (by reducing friction and weight).

0.https://www.youtube.com/watch?v=rwt9K9PWMcU

It's a hyperloop!

A Simple Electric Train (2014)