Not sure why it matters:
You showed clearly in the video that the device uses BB/TI PCM2704 USB audio DAC. That IC implements standard USB 1.1 Audio Device Class. Therefore it should work, regardless of VID/PID, with any modern operating system.
The only USB devices that do not work with Linux are those with proprietary protocols.
The SMSC USB2512 is interesting, however. Is it used to change the VID/PID, or to multiplex a second USB IC? Is the volume control soft (via the PC) or hard (in the speaker)? PCM2704 appears to support soft volume anyway.