LIGO detects length changes of 10^-18 m, or attometers, not femtometers, which are a thousand times longer. (https://www.ligo.caltech.edu/page/facts) But this does not matter at all, because this is not resolution of the body image, but the size of the vibration on the speaker. That's a technical data point that I don't see any reason to include in this presentation other than to cause this exact confusion.

The video looks in general like it's trying to impress by giving a lot of incidental information about how the device works while being very light on what it would be able to actually see -- e.g., it doesn't matter how many gigabytes your device collects if the resulting image is blurry.

Compare the website of LIGO (https://www.ligo.caltech.edu/page/facts), which also has a lot about the technical marvels (huge vacuum tubes! precision engineering!) but crucially includes the goal of this all.