How does this work?
Not the way you want it to.
100BASE-T Ethernet only uses four wires.
So that leaves four unused wires in a Cat5 cable.
Several ADSL modems provide both an Ethernet and a USB connection to the host PC through a single RJ-45 connector.
A brand of UPSes also uses a similar RJ45-to-USB cable. See Can you help me identify this USB cable?
Does it require drivers or a specific OS? If not, how is the USB protocol sent over an Ethernet port? I'm considering doing this to attach a keyboard to a motherboard on which all the USB ports died.
You are completely misunderstanding the purpose and application of this adapter.
It does not allow you to transform an Ethernet port on your PC into a USB port.
If you do not have an ADSL modem that you prefer to connect by USB rather than Ethernet, then this adapter is of no use to you.
Apparently you're asking an XY question.
USB is a bus, to which you can attach other devices/controllers, whereas the Ethernet controller must attach to a bus.
There is no method to turn a network connection (e.g. Ethernet) into a bus (e.g. USB or PCI).
The motherboard has to be repaired or an expansion board can be installed to provide new USB ports.