Unfortunately, I think this must be a coincidence.
The fact that you saw the sign-in Window (but without the actual sign-in form, only the window background) means that your device was not signed-in or "linked" in the first place.
Also, if you try to sign-in on a 3rd device with a free account, only after providing the user credentials the system can identify you and check how many devices are connected - we definitively do display an appropriate message regarding the device limit if required.
There must be another root cause to the issue.
What else did you do after "unlinking" the old device?
Did you maybe re-install Boxcryptor or delete the settings folder?