It is unlikely that the zip file is the correct file. Iirc those fire tablets run android and are somewhat restricted. You need to find out if and how you can sideload apk files on that device and retrieve such an apk. Just make sure the source is trust worthy ( hosted on itch is not trustworthy in itself).
If this is some emulator thing, there are some games that can run in some kind of emulator. I have seen games here, where the developer does not create a separate apk file, but users managed to get the game running. I think it is for rpg maker games.