With my DLP printer in mind, I wanted to redesign the original model, so that I could print a complete model and cone in 1 pass. (please read on.. there is also a FDM print)
In the video it was showed that if you put 2 tracks together, the cone always goes to the "highest" point and eventually comes to a stop there. 

So I designed a double track. I increased the angle of the cone to 45° so that I had a narrower track that was easier to print with the small bed of the DLP printer. At the cone I removed the two sharp points and created 2 flat sides which serve as adhesion to be able to print the cone in 1 go. I provided also the track itself with a radius.

Because I wanted to make the model as smooth as possible, I printed 2 axles that I attached to the ends of the cone in turn with superglue. I was able to finish everything super smooth with fine waterproof sandpaper. Afterwards I carefully broke it loose again and sanded the ends.

All parts fit on the bed of my DLP printer (130x78mm). I have attached the print file as a zip under [Other Files]. Printing time is 2h46m.

After all this was successful, I also wanted to see if this could be made (without supports) on my FDM printer. Because the model is quite small, I set it to 165%. The length of the model is then almost 180mm. It printed also very well. For a smooth movement you need to sand the track. Use a skirt to print!

The printfile and STL files at 165% are added.

Scaling allows you to extend the length of the track. However, don't scale in height or width! It only works if the ratio between cone and track height and width remains the same.

p.s. The STL files for DLP are quite large, partly due to the very high detail.