I suspect you are going to be installing 8.0, activate with the key, then run windows updates until 8.1 is presented in the store app, then upgrade to 8.1, then run windows updates to get 8.1 up to current.
Remember if they made it easy and allowed you to just use the key you paid for and install directly to 8.1, they would no longer be emulating apple, and that is not part of their plan anymore.