If this ruling would have been in force back then, Nixon could have argued that the conversations were done in his official role as president. For example, a conversation with his chief of staff about ordering the CIA perform a coverup could be considered “official business” since he was talking to a top executive branch official and directing an executive branch agency to take an action.
The distinction between “official” and “unofficial” becomes meaningless when a president can use their official powers to do illegal things that benefit themselves in an unofficial capacity. Hence the absurd conclusion that, apparently, a president cannot be prosecuted for assassinating their opponent using Seal Team 6.