Update.
On Windows 7 driver installs, then monitor detected properly and everything works. So it's not a hardware issue.
Also on Windows, I can see DisplayLink device detected in both Audio and Video category. As far as know, on Linux DisplayLink support only Video interface. Would presume in my case, that on Linux installation script install Audio part of the driver instead of the Video part.
Will try to go deeper into installation script, despite I'm not an expert... Any advice and help still highly appreciated.