These are the processors supported by Windows 10:
Your stick is not an Intel product, so you will have to speak with the manufacturer.
Regarding W10 Enterprise, and I think you already know what I am going to say, is "why"? Nevermind, do not answer.
As for the rest, ask Microsoft regarding W10e on this "other" stick.
I have never seen Windows 10 Enterprise shipped on one of these sticks -- but this is because most of these sticks are targeted for the very low-end of the market and thus their (memory, etc.) configurations are targeted to stay at or below the thresholds set by Microsoft for getting the Windows 10 Home license very cheaply.
I see no reason -- well, other than most of these sticks only have 32GB eMMC SSDs and 2GB of memory (or less) -- why you couldn't install Windows 10 Enterprise onto these sticks. Windows 10 Enterprise is a subset of Windows 10 Pro and I successfully upgraded a (Intel) Compute Stick to Windows 10 Pro without issue.