I spoke to someone at customer service and it seems like they might make an exception for gifted kindles. Call the number listed at the bottom of the product description and speak to someone. They are very helpful.
They (Square Trade) actually told me on the phone that they have extended the amount of time that you can decide to purchase the warranty to 90 days after purchase date. I know it doesn't say it here, but that's what they say at Square Trade.