The paid for feature seems to show the number of dislikes that have the extension installed, however what is shown is the estimated number of dislikes based on the actual number of likes youtube shows, so if the extension users have a like/dislike ratio of 50%, and there youtube shows 1000 likes, the extension estimates that there are also a 1000 users that disliked the video, even though there may only be 1 like and 1 dislike from the extension users, which would be very obvious that the estimate is very off.
IIRC, in the earliest days, the extension reported the dislike count that was still in the API but not surfaced in any clients. At some point after that, Google removed the count from the API entirely, requiring the current piecemeal approach.