W5100 is by Wiznet (South Korea). A nice company to use for embedded Ethernet controllers.
The Intel Galileo uses its own CPU (System on Chip or SOC) of the Quark SOC X1000 series. Respectively, the Ethernet controller is built inside of this CPU. Also an aside, really doubt that Intel would need to use the Wiznet controller since Intel is more than able to design their own Ethernet controllers and have done so for many eons. The Quark CPU datasheet should offer more details on the Ethernet controller.