A Lissajous figure is what you get when both the X and Y positions of the beam (or virtual beam) are controlled by sinusoidal oscillators. This is using the same XY mode on the oscilloscope as used for drawing Lissajous figures but it's not a Lissajous figure itself.

Technically (loosely) the way the ball (circle) in the game is a lissajous figure; it uses a scaled sin and cosine signal driving the x and y input of the oscope to create it. It's one of several signals (mainly on the y-side) that are mixed down (done in a similar manner to a simple op-amp backed audio mixer circuit) before being sent to the scope input.

It's more like a custom homebrew analog computer with a few unusual additions.

Seriously impressive.