So why does the new AP shiv get scaling?

AD Shiv can crit, AP Shiv does not.

Because it doesn't scale with movement as much as shiv, and it only gets stacks on spell casts / movement.

Since the normal AD Shiv already has scaling due to autoattacks getting the charge up more? Or maybe because the AD Shiv already scales autoattacks well (with AS and crit, which are multiplicative)? Or maybe because the AP Shiv is otherwise a pure stat stick, which Rabadon's already fills the role of?

It's not that much. At 1000 AP it only does 50 more damage than a crit on statikk shiv.