That's not an ICSP header. That's the interface between the Ethernet adapter and the Arduino (via the SPI interface). That ENC28J60 chip does the Ethernet interface but unlike the newer Ethernet shield it doesn't have the TCP/IP stack in hardware. You have to use the older Ethernet library that included the software TCP/IP stack.
Perhaps this article will help: http://hackaday.com/2012/07/10/cheap-as-chips-arduino-ethernet-shield/
Or, for about twice the price, you can get an Ethernet Shield with a WizNet W5100 chip that works with the current standard Ethernet library and examples.