That is, instead of using y velocity = acceleration * time and then adding in gravity, they made something like this, as I understand it:

speeds = [0, 1, 2, 4, 8, 4, 2, 1, 0]

And then you keep track of how many frames it's been since you jumped, and then just do

yVelocity = speeds[ticksSinceJump]

No math needed at all.