Ethernet connector and transformers
No, that jack is not a Magjack. It is a bare connector. I say that because the chip next to it is the Bel S558-5999-46. It's specific datasheet is here. It is an Ethernet 10/100Base-T Lan Magnetic Single Port Transformer. You could use that. Or both the chip and the jack. It should be compatible with the ENC28J60, most common 10/100 magnetic transformer would. The S558-5999-46 is a 1:1 Ratio transformer. See the schematic below for tappings and pinout.