@jdpappadeas - I think what you're missing there is just adding the "combine" operation is not necessary.
Just arrange the shapes - draw a rectangle over them - (don't have to worry about combining them or filling all - just fill the rectangle) -
Then Select all the shapes including the rectangle and click: Divide.
You should have it divided into it's constituent pieces - all filled red.
I'd suggest trying it with a simpler shape so there aren't so many variables as to your expectations. AD can handle very complex shapes, but it can be confusing for us to sort out what our expected result is if there are too many intersections etc.
If you'd like - I can attach an example with my results (they are very similar to the video - but I think AD is stronger with it's boolean operations). Inkscape is looking much better than the last time I used it for sure too!
the dartboards go from #1 - overlapping circles similar to what was shown in the video to #6 - showing the finished, cleaned up result.
there were more artifacts in the process than I'd like, but the Divide command did work successfully for me.