What is this networking device?

I have ethernet port and coaxial port in every room and they seem to be branched out from the low voltage box in the master bedroom. My Comcast gateway device is connected to the coaxial port in one of the rooms and it functions normally.

I found this device in the low voltage box that seems to be terminating all the RJ45/RJ11 ports in the rooms. Is this device a hub? If I connect the ethernet port from my gateway device to the ethernet port in the wall that eventually comes to this unknown device, does it provide network connectivity to all ports connected to this device?

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As @Tetsujin noted, this device is not a networking device, it's most probably distribution frame for telephony service. Distribution frames are mostly used in larger scale installations to terminate telephone/network connections in a central location. Think patch panel, but then the older version.

It's a completely passive device, only electrically connecting wires together. It won't give you "ethernet" because it's not a switch or a hub. You could, with the appropriate tooling, use it to route wires to a switch or a hub. That said, the distribution frame was probably made for telephony service and wouldn't provide good data rates (in addition to the problem of the cables only having 2 wires).

If you own the house, I'd replace the wires with cat5e/6 Ethernet through the existing conduits and terminate them in an RJ45 patch panel. Then you can use a switch to tie all the rooms together in a central location. If you don't own the house, check with the landlord and see if they'll allow you to replace wires or modify the existing setup to run ethernet over it.