I have three of these, if they are the same, having what looks like a power adaptor connection on the opposite side to the USB ports.
They seem to work OK on Jessie 4.1.19-v7+, with one drawback.
They all report the same MAC address, 00:e0:4c:53:44:58, which is problematic if you have more than one on the same network.
For a partial fix for this, I added a pre-up script into /etc/network/if-pre-up.d to iterate through the eth? devices, and on finding a "broken" adaptor, assign a new address to it (which is actually derived from the Pi serial number, like the smsc interface does.
It's not "that" robust, since it only works for the device connected at boot time, and only works for one device on the Pi, but it solved the problem of having multiple Pi zero/DM9601 connected devices on my LAN.
The nuts and bolts of it are simple. Run ifconfig ethX (where X is 0,1, etc). If that succeeds, the adapter exists, so run ifconfig again, and use grep and sed to extract the HWaddr part. Check it against the bad MAC.
If it is the bad MAC, then generate a new mac (again by judicious use of grep/sed on /proc/cpuinfo and the serial number line), and then assign it a new hardware address.
Since ifconfig is now deprecated, I should really work out how to set the new hw address using ip, since all the other stuff is possible....
No, I can't think of anything funny that won't offend someone if they want it to...