So this depicts the Arduino EtherNet module, connected to the micro SDHC slot?
Assuming that is the case, which low level protocol is being used to send TCP/IP and UDP packets through the micro SDHC slot / cable?
Actually, the Arduino-centric version of these modules is not recommended. The Micro SD slot runs with 3.3V power supply and signal levels, while the Arduino modules have a 5V VCC (and sometimes clamping diodes that might be harmful to the Vampire board). A plain 3.3V version is better in this regard as it doesn't require soldering on the ENC28J60 board itself.
The layer1 protocol is straightforward SPI at roughly 20 MHz. Some modules also accept slight overclocking (up to 23 MHz).
The payload at layer2 is IEEE802.2/802.3 Ethernet in conjunction with a SANA-II driver. This way, one can transparently use any networking stack with Ethernet support. The MAC address is auto-generated from the Vampire FPGA serial number.