This is extremely well-written. Kudos!
Basically all 8/16-bit console graphics tricks take advantage of one (or both) of the following two facts:
1. 8-bit and (particularly) 16-bit consoles are built to draw and move 2D tiles crazy fast. If the effect you want can be achieved (or faked) by a series of animated tiles, you can do it. The most obvious example is "segmented" characters (usually bosses, but also the protagonist in Vectorman) that are made up of multiple sprites (tiles) that are animated in such a way as to fake smooth 3D animation
2. The screen is drawn one row at a time. Left to right, top to bottom. Like a typewriter. You get a little bit of processing time after each row, and a little extra time after the last row. You can use this time to tweak things (like, the position of the background, or the position of a sprite) in between rows. This is how you can achieve "line scrolling"
"Simple" line scrolling where you change the background scrolling rate on each horizontal line, for a very smooth effect: https://youtu.be/hIiMz_NUDEw?t=97
More advanced line scrolling where you manipulate both horizontal and vertical scroll in between lines: https://www.youtube.com/watch?v=QN2Yoz0INrI
I am not sure, but I think many of the abstract effects (not the polygon animations, which use tile rendering) in the Over Drive 2 demo that this article discusses are achieved by extremely precise manipulation of sprite positioning and/or scroll registers as in #2 above.