I found the solution!

Thanks @CarltonR for idea to check behavior of other VMs, and good that I'e had one.

I've compared configuration files for two VMs mentioned before: created in older version of VMWare Workstation and newest one (at the moment 16.2.1). There were some differences caused by a way of creating VM (I suspect that I've created old one without using VMWare's Easy Install), but that's not the case, I assume.

I've found one very interesting line in "*.vmx" configuration file:

usb.restrictions.defaultAllow = "FALSE"

It's very interesting because looks like it has been added automatically in the VM creation process, and it is NOT configurable from the GUI. I am considering this as a major flaw, but don't know how to report that problem to VMWare bug-tracking team. Also, there's not enough documentation about configuring VMs directly in "*.vmx" files, all of the docs I've seen so far are explaining configuration in GUI only.

After deleting this line from VM's configuration file all listed USB devices became able to be connected to VM. Problem solved.

tl;dr

Open VM config file (with ".vmx" extension) with a text editor, find line mentioned above and delete it completely. Do this when VM is powered off.