Line pictures in Corel.

I too have wondered how to do this and have been looking at options.  One benefit of such a process for me would be you could make a photographic effect from one color of cut vinyl.   I don't know of a quick technique in Corel Draw to make this kind of output.

For this to work the strips, groves or patterns have to be something the machine can handle.  I think this was your intention as the video you posted was from a vinyl cutting program.

pranderson's suggestion is good for getting the visual effect but it is a raster solution. If you are in need of pure vectors to generate cutting paths it is not complete.  There is another raster option that gets close which is a Gimp plugin found here:  http://pages.infinit.net/leware/engrave.html

Using either maybe the results could be traced to get a vector output.

There is a program called Project5 purports to have this capability.  It is around $300.  Here is a sample image so you can see how the cutting paths looking up close.  

Now, the newcomer and it's free!!  At least it's new to me as I have just recently started fiddling with it.  ZebraTrace.  http://maxim-s-barabash.github.io/ZebraTrace/  It produces SVG files.  I still haven't completely wrapped my head around it and documentation is scarce.

There is also PhotoVCarve for about $150.  http://www.vectric.com/products/photovcarve.html