it says on that mediasonic link
Important Note: • For eSata connection: Make sure your eSata port Support port multiplier. Most onboard eSata and some eSata PCI-E card only Support up to 5 drives. To see all 8 hard drives in eSata you need a eSata PCIe card that supports 8 drives.
I'm assuming the enclosure doesn't do any of the raid/array configuration, it just passes data through.
as far as I know only USB and eSata can do port multiplying. I think if you want to get access to all the drives you'll have to get a pcie card to handle the eSata or just use USB3. eSata (6gb/s) is faster than USB3 (5gb/s) and you might actually manage to saturate the connection trying to read or write to 8 drives though one cable.
in your use case both options are less than desirable but esata (if done correctly) could be faster. USB3 will probably be fine unless you really need that extra gb/s of speed
Edit: It looks like sata port multiplying can exist but its not really supported by manufacturers nor required by the standard so hit and miss as to whether a board can handle it.