you can do some form of index painting on ProMotion, but that wouldnt reallly be equivalent to this.
You can use promotion to draw with a brush that can draw with different blending effects in real time, if that's what you want out of this you can do that with ProMotion, but that isnt really what Indigo is talking about here.
The big thing is the "non commital" part that Indigo keeps emphasizing, that's exactly what adjustment layers (you called them effect layers) are about. What's different about this is you're basically drawing within a color ramp with normal photoshop tools, and you get to decide after you've drawn it how many shades it should have, what hueshifting it should have and chose between a variety of dithers.
I know how I could set up all the layers in photoshop but I still dont think I'd come out with the same results as indigo, he has acquired a certain level of comfort with this tool that anybody just trying it doesnt have. That's the part that many reading the tutorial might not get, it takes a very specific way of painting to get this to look right, this is isnt a shortcut to drawing tiled backgrounds of the level of quality that there is in the Owlboy game or Indigo's work. Like indigo said, just a tool.
I suppose what you could do in gimp is find an alternative for posterize and alternative for gradient map and apply those effects on an image you've drawn in grayscale. if you know exactly how you have to draw it every time I guess you could come up with similar results but you wouldnt be drawing pixelart with "dirty" tools in real time.
Dont you have any friend that has photoshop CS3 or higher? just take the psd to his house and mess around with it, you'll see what it is about, you'll calm your curiosity and know whether you NEED this or not :p