Ethernet hookup question

I have a show coming up where the venue has a rig requiring 1 ethernet out from the controller to control 4+ universes.
My controller is an ONYX PC, where I have this show configured on Capture and all is performing correct, including the required 4 universes. With this system I have a one key license capable of 128 universes, and a couple of these Obsidian NX USB to DMX licenses.

My question is: Can I connect the Ethernet out from the PC directly to the house (rig) “ethernet in”? Or do I need a separate interface from the USB to convert to Ethernet?