Problems trying to sideload app onto Amazon Kindle

[LaughinGrass]

I bought this app about a year ago and I really love it. Recently though I've had a problem trying to sideload the game onto my kindle. I can't legitimately download it from the play store as Amazon is stupid that way. So instead I pulled the apk and uploaded it to my Google drive, which I then redownloaded onto my kindle. As I thought though I got the licensing error. Is there any way to sideload this app legitimately through Google play on a kindle?

[Exophase]

It needs Google Play to operate, so the only way to get it working on Amazon's devices is to root them so Google Play can be installed.