They may be a definite answer out there, but I suspect he uses Gimp or another similar image-editing program such as Photoshop, which are not "simplistic area[s] to diagram," rather, it looks that way because he crops the screen-cap to only show the drawing area. Notice how the cursor sometimes moves offscreen, then when it comes back, it draws in a different color? This is why I think he uses some image editing program, as he's likely picking the new color from a palette.
Edit: I am mistaken. They (Sal at least) use a program called SmoothDraw, which looks to be exactly what you want. Source
Cheap tablet with stylus (this one's only about $30 on amazon: http://www.amazon.com/gp/product/B0049BY6FQ/ref=oh_details_o01_s00_i00) plus Smoothdraw: http://www.smoothdraw.com/ (same program used for Khan Academy vids)
Whiteboards are pretty useful, and I'd never been a big doodle fan before then. Once I found out how expensive dry erase markers were, I gave a tablet a lark. Works great!
You can get her a Genius MousePen i608 ($58 at Amazon). It is good enough for a beginner (I have one).
Try SmoothDraw and ArtRage Starter. Both are easy to use and free.
That software reminds me a lot of the one I saw Sal from Khan Academy using. I don't know if it's the same one but it looks like SmoothDraw. For the recording, I'd use OBS Studio
Hello! Khan Academy has an article for this!
Sal currently uses a computer with:
Before that he used:
Enjoy your summer!
What Khan Academy uses: https://khanacademy.zendesk.com/hc/en-us/articles/202483430-What-software-program-equipment-is-used-to-make-Khan-Academy-videos-
Some free alternative drawing tools:
I watch my regular subscripted Youtube channel video's and draw on Smoothdraw ( painting software ) and 3DS Max :)