The science behind table tennis?

Kinetic energy.
Electromagnetic force (i.e. low-speed elastic collisions between solid objects, and tangential frictional force imparting torque and rotation), and of course gravity.
The main thing that’s unusual about ping pong is of course the rigidity and lightness of the balls compared to their size, so that very subtle differences in the force of a stroke have a big effect (in contrast to Badminton, for example). Also the greater size means more relative air resistance (friction with air) compared to a denser ball.

Also, for the case of someone like me who has difficulty not hitting the ball too hard, there may be a buildup of psychic energy from frustration and/or hilarity.

I agree, Zaku. Sometimes there is a localized “cursing force” involved.

The magnus effect link