This is what I see immediately below the "Write a review" button (which always appears after the last visible review) for the paperback version of Alien Bonds:
This is what I see below the "Write a Review" button for the Kindle version of the same title:
It just goes right into "what else did customers look at" list! No button for hosting a giveaway!
On the other hand, I just successfully hosted a giveaway of a Kindle book by using the "Copy This Giveaway" button that appears on my Completed Giveaways page. Ergo, the functionally still works for Kindle books, but the buttons are gone. There's no mention of this that I can see on Amazon's Giveaway FAQ. In fact it still lists Kindle books as being eligible, so who knows if Amazon is really killing it or somehow the buttons just got deleted.