Does it actually work?
Yes, it's just filtering and it appears to be mechanical, rather than electrical damage. If the windings are intact, then it should work, although its ability to filter noise will be affected, in which case the device will still work, but could be more susceptible to noise and/or be more likely to produce noise, including that which could interfere with other devices.
It does still work but if it isn't filtering out the noise as it used to it may need to be disposed of since that is its main purpose. 
In my honest opinion, this AudioQuest device doesn't have a purpose and may even degrade the USB signals to a point where the transfers are slowed down due to frequent CRC errors. And I'm talking about a new, undamaged device here. AudioQuest sells unnecessary and junk devices (in other words, snake oil) at insulting prices. Let me elaborate on the usefulness of ths device in particular:
USB is kind of "mixed signal". The encoded signals are digital in nature but the signal conditioning is analog, due to the need of employing pre-emphasis and equalization for varying signal rates. Your device may act just like a very long cable and just add inductance and capacitance. It will do nothing to improve the signal. USB doesn't need "filtering" or whatever the device does.
You can do a simple test. Grab a fast USB flash drive and do a transfer test with and without the bogus device in the middle. If you have a slower speed with the device in between, there you have it. For sure, you won't get a higher speed with the device. And that's irregardless of it being broken or not.
P.S.: By the way, by looking at the PCB I see that the differential pair was not designed with care. I doubt it was designed according to the USB specs, that is 90

differential impedance and 50

single ended. The traces are definitely too thick for a 4-layer board (assuming it is) and there is not enough clearance to the ground plane. Clearly, the designers know nothing about electronics and signal integrity.
Kind regards, Samuel Lourenço