It has been pointed out to us, that group plugdev is specific to Debian-based Linux distributions.
This causes the Udev rule in the manual incorrect for users of other distributions.
We should therefore try to find a distribution agnostic solution to manage WebUSB device permissions.

After a brief research I discovered a uaccess tag based approach is considered by many as preferable to group based.
Applying TAG+="uaccess" instead of the previous MODE="0660", GROUP="plugdev" should allow the current session user to access the device.
This same issue was presented to this project.