Yes. You can also see that the magnet is reluctant to move AWAY from the copper block when it's drawn back (the zoomed-out part of the video shows that best).
Whenever a magnet moves relative to a nearby conductor, eddy currents are induced in the conductor - and those eddy currents set up a magnetic field that opposes the magnet's movement.
If you've got superconductor so that the eddy currents can flow without resistance, you can levitate magnets over it - or levitate the superconductor over a magnet.
With a regular old copper block, the eddy currents do encounter resistance and quickly die away - so it behaves more like a shock absorber for the magnet than the 'perfect spring' behaviour of the superconductor.