EDIT:: My point being that I don't particularly believe that if the minigame had not been included it would have made a difference in the enjoyment/number of backers.
Out of sheer curiosity, and not because I want to continue arguing (really, I'm simply curious), when you ran the poll did you ask
before you created the minigame whether your patrons would like minigames in your game, or did you ask after the fact? That, too, drastically skews results. Polls are tricky things.
@PoisonJames' last post details one of the many ways that a poll can fail to be useful. Which questions are asked, how they are phrased, who is asked, how big is the sample, and when the poll is run all impact the result. Again, as
@PoisonJames pointed out, if the intent of your poll was affirmation that your patrons approved of your decision, then mission accomplished. However, you probably didn't need a poll for that. Just seeing if your patron count went up or down would suffice. So, in that regard, the poll is pretty useless.
And with that I think that I've beaten this particular horse to death. Thanks for listening.
Also, if you don't think that having a minigame changes the number of, or enjoyment by, the backers then it begs the question of why put it in? I'd think that the sole reason for adding a feature (any feature) to a game (any game) is because it improves the game somehow, from the perspective of the game's players. Because if it doesn't then there's no point to do so. Just saying.
