> Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time

That's not correct. There is a relationship between the radial coordinate r you are at and the time it will take you, by your clock, to reach the singularity (at least assuming you are freely falling), but that relationship can't be described the way you are describing it.

To put the issue with what you say as starkly as possible: at any event inside the black hole's horizon, there are spacelike curves in every direction from you that will hit the singularity! So "the direction in space between you and the singularity" is not even well-defined.

To be clear, you are right that Susskind's statement is very misleading (I posted my own criticism of it upthread).