So, as I am writing the build instructions, I get to where you are installing ESXi.
On my testing prototype system, the GB Lan is a Realtek 8111 - for which there is no driver in ESXi and the install FAILS.
I used the ESX-Customizer (which I will link to in the build instructions) to inject the RTL8111 driver (a VIB file I will also link there) into the VSpere install ISO.
However, the H81M-ITX specified has an Atheros 8171, for which there is NO VIB file to inject. Until I get one in my hands, I can't really say if it will work or not.
The H81M-ITX/Wifi , while a little more expensive, has an RTL8111, so I can say for sure it will work.
Plus it has a potentially available PCIE 1x available for some pass through device, maybe we can replace the USB-->SPDIF, or add a second display (limited to 1x)