Here it is the end of February and this issue in 5.1.0 has yet to be resolved? I'm finding the same issue with the Realtek 8111E NIC embedded onto the motherboard. After looking at the many log files and entries generated I believe there may be a of hint of reason for this NIC not functioning. In the VMkernal logs it shows at installation time it could not determine the correct hardware and chose to use the 8111B drivers. There may be something significantly different with this driver than the E version of chip.
I have installed a much older Realtek NIC in one of the PCI slots and everything is working fine, excluding the 8111E NIC.
It appears I have no other choice but to try the 5.0.0 version and see where I can get with getting this MOBO up with the onboard NIC.