I installed the iOS Rekordbox app and did a password reset request from within the app. Received the email, clicked the button on my mobile device and entered a new password. Logged in to Rekordbox fine!
Some observations that may give a clue as to why it worked by initiating the password reset from iOS:-
[fails] Desktop Rekordbox password reset email links to - https://www.pioneerdj.com/Account/NewPassword/?apiKey=
[works] iOS Rekordbox password reset email links to - https://www.rekordbox.com/account/newpassword/?apiKey=