It looks like it didn’t save the key to slot 4 permanently, you can use -k 2020666666668888 instead
I think you can manually save that key to one of the slots with the hf iclass managekeys command, but you’d have to play with it
Those readers can be used with a variety of different iClass credentials, and not all of them can be cloned, at least not that I’m aware of
I unfortunately don’t know enough to tell the difference between them just by looking at the dump, though if I had to guess this smells of SIO to me
(Here’s a thread that touches on that subject: HID Iclass Legacy 2k FOB with a HID iClass SE Reader R10)
Fortunately, the guy I’d go to for iClass and HID systems I already pinged earlier, so hopefully he’ll swoop in and help out 
In the meantime, I think if you run a hf iclass decrypt -f hf-iclass-FDCC6111FEFF12E0-dump.bin it may help narrow down the options