There is a segment in the video where a fiber is glowing like crazy with near IR, as it cuts hairs on a guys arm. This shows as whitish violet on color cameras as it gets past two dichroic filters in most cameras, one red, one blue, but usually not the green in the CCD mosaic. It is cutting hair on the guy's arm. From past experience, lasers in the 700 nm region usually hit the red pixels in color camera, and lasers in the 808 region hit residual responses on both red and blue. That strongly hints that the test laser is around 800 nm.
This is a bit of voodoo on my part, as no two models of color cameras have the same filter Reponses, and most have a IR cutoff filter in front of the CCDs. Better cameras cut IR entirely. Standard Silicon CCD response falls sharply to zero at 1100 nanometers, and CMOS cuts off even earlier. I have no idea what camera they used. We use off the shelf silicon CCD cameras to examine and aim near IR laser light in labs. While the response is hardly optimized for near IR, it is a low cost way of doing things. For that reason I have a good idea how various cameras react to wavelengths they are not designed for.
So there is either near IR 752 nm pump light in the fiber if the fiber itself is doped with rare earth and is lasing, or the test laser in the video was in the 750-850-900 nm range. Rare Earth Fiber lasers line up with some of the near to mid IR wavelengths mentioned in the patent, but cost and complexity of the needed optics plus the need for another laser diode to pump the fiber gain medium, suggests this is unlikely. It would have an advantage with the evanescent coupling as you just put a mirror at the end of the fiber laser and allow resonance to build up inside the optical cavity thus formed. But that is so darn "out there" as to be highly unlikely.
I've never seen short fibers lasing either, usually the length is in the 10s of meters to a kilometer.
There are very few affordable diodes at wavelengths greater then 1100 nm, and few high power diodes at 1300-1500 where there is a market for diodes for long range fiber communications. There is nothing inexpensive at wavelengths greater then 1500 nm.
As I doubt you can get a Erbium fiber laser to useful powers at low cost in such a small space, and based on the video, I'm betting on a IR diode laser at less then 900 nanometers... But longer then 750 nanometers...
Ockham's razor, plus an educated guess, suggests the video shows a near IR diode laser directly coupled to a fiber...
Steve