Basically the ADuM3160 and the ADuM4160 are the same functional wise. The only difference is the certified isolation rating, as can be seen already on the front-page of each of the data-sheets.
The ADuM3160 is only 2.5kV rated and the ADuM4160 is certified for 5kV.
I quickly tested a original Arduino Uno Rev 3 with our ADuM3160 Evaluation-Board, which looks similar to the schematic you linked to (but with ADuM3160) and it is working perfectly on my Laptop.
If you use a Desktop, sometimes the power-supply on Desktop-USB-Ports isn't as good as on Laptops.
So first of all check the Voltage on the ADuM5000 input and the isolated side, that this is working on 5V correctly.