Not sure what the value of running ESXi on a board that only has 4 GB of memory?? What goal were you trying to accomplish. Perhaps using Windows 10 with Hyper-V is a better option, or linux with KVM. At least on those, the main OS is still available for use. ESXi really is designed for machines with much more memory.
David, I'm trying to get vSphere ESXi on the Up2 and have hit the exact eMMC Storage issue you had. Did you ever manage to overcome this? I can install it using USB drives but this not ideal.
I can't find any option to create a datastore on the drive that holds the ESXi-partitions.
Update: on the Up Squared with the latest EFI/BIOS Update (3.3, maybe earlier version works too) the above mentioned bug that no video is available when booting the ESX is not present anymore.
So you could install the ESX without the need of a virtual machine to setup everything. I think that's great :-)
Edit: correction: it will show Graphics Output, but only until another step. Well then, everything stays the same, you can run ESX (tested up to 6.5) on Up and Up-Squared, but you have to install it using my instructions above.
Edit 2: it seems, after fiddling a bit with the settings, that the Up Squared can fully boot ESX 6.5 even with graphics output. Great again :-)
Here you have a first PXE boot tutorial for Linux on UP platforms: