What an amazing marker that is, that changes ink colors spontaneously.  It's magic.

1.  Get a graphic artist to draw, shoot that, and speed up the video in post.

2.  Shoot a still or video of a hand holding a marker, mask it and animate the pen tip over a Write-on / masking reveal (or reverse conceal) from previously drawn art.

3.  Use the record feature of Painter to record illustrations being created, and animate the masked marker tip as the image is revealed.

Method #1 is the quickest to pull off in post, but requires a pretty good illustrator to draw in real-time.

Method #2 was probably used in the sample you provided.  Look at the fonts.  They're all the same; and some of them are fonts people don't ordinarily draw in freehand illustrating.  If you look closely, you can see that an artist filled in some traced outlines of what appears to me to be computer generated fonts and clip art (Look at the two bananas; nobody draws two bananas by drawing the back one first, and adding a second one on top.)  And look at the pen position in the hand; it doesn't change much.

Method #3 requires an expert in Painter, and I don't know any.

We ended up going with #1.  The biggest post challenge for me was to control and match the shadows cast by the real arm on the real drawing (even after trying to banish all shadows using several soft lights).  In retrospect, we should have prohibited the people (camera guy and producer) getting close to the artwork while shooting (Producer was pointing where and what to draw.), as the white paper picked up fabric colors that were bounced from the lights onto the paper.  Everybody around the paper, including the artist should have worn all black.