The main difference in processing power compared to the shuttle is that it's not using a Mk 1 astronaut as a control system for the landing.
I suppose the relevant sensors have got lighter and cheaper, and I assume there's precision GPS being used that wasn't available until at least the 90s. But I expect there's also a cultural element where it really needed someone who didn't remember how crashy the
LLTV was, and who could get over the "aerodynamic braking doesn't need any fuel" paradigm
[1] to come along and try it.
[1] Bear in mind, SpaceX have been working towards Mars from the outset. They *need* the powered landing for that in a way that previous earth-based systems don't.