The EVGA Tegra Note 7 does not look that good to me. While it has an Nvidia Tegra 4 processor, it only has 1 measling GB of RAM. And the resolution is only 1280 x 800. And as far as I can tell, the Qualcomm Snapdragon 800 is by no means inferior to the Nvidia Tegra 4. The Kindle Fire HDX (7-Inch) has a Snapdragon 800 processor with Adreno 330 GPU (Not that it could have any other GPU lol), and it has a 1920x1200 resolution, which I see as superior. It has 2 GB of RAM. The only thing that really bugs me about the HDX, besides coming shipped with Fire OS, is that it lacks a microSD cards slot. BUT, it has a USB 2.0 port, which is also quite useful, and comes with up to 64 GB internal storage. So far, there has been no way to get AOSP on the device for a better Android experience, but there is a fair chance it will make it to the device sometime. In the mean time, it should be fairly easy to replace the launcher with Nova, if you dislike the stock launcher, and should not be too hard to get the Play Store on the device. As always, side-loading apps or downloading them off the internet should be simple enough. And of course, you can already root it and use a custom recovery. In short, the Fire HDX should be better for gaming and everything else.
You can find threads for what you are looking for on XDA under General, Android Development, or Original Development, etc.
http://forum.xda-developers.com/kindle-fire-hdx
I suggest waiting for a deal on the 32/64 GB models. Last one was Cyber Monday. There is a deal today for Green Monday but only for the 16 GB variant.