Help with network connection

The fact is that the old live has no inbuilt WiFi capability, it needs a supported adaptor to work. Its all to do with what WiFi chipset the player firmware supports. As you know on the PC you added the driver for the adaptor, that same requirement has to be in the firmware. Unfortunately the adaptor manufacturers keep changing the internal chip sets without changing the actual model number and equally unfortunate is the fact that the old live player is at end of life.
The newer Live Streaming player gen3 has WiFi built in like your other gadgets and therefore would connect just like them. As you see WD have done the same when it introduced this updated model.