Now you can, well sort of.
I've edited a playthrough of the game as a TV show, cut into 16 parts. I know it's not perfect but I hope it's good enough. I didn't want to spam the forum with each part so I figured I would wait until I was done with the whole "show". I uploaded the first part Jan 15, and today, one month later I'm done. 100 hours in the making. (Each part is about 15 to 30 minutes, 7 hours in total)
You can find the playlist here
There are just one or two gameplay moments in the first part, and the "cursor" pops up a couple of times. But as the "show" progress I got better at finding new ways to cut them out and "hide" the cursor in all scenes.
Hope you like it! :)