Hello Michael,
This PID 0xa213 isn't from the DisplayLink chip. The VID is 0x17e9 and the PID will start with 0x6.
Are you sure the video output was doesn't need enabled by an app before being visible?
The manual p29 mentions the output is disabled by default.
It's possible Bose is controlling the video function by enabling/disabling the DisplayLink chip in the product. That'd explain why the DisplayLink Manager app doesn't see the chip.
Regards,
Alban