I purchased Final Fantasy 3 and 4 for my phone awhile ago and wanted to try them out on my Nvidia ShieldTV. I can download them fine from the app store on the Shield, but when I go to open them, there's nothing but a black screen and no audio. Pressing the back button will bring up the dialogue to close the app, but that's about as much interaction with the games as I can get. I can uninstall and re-install all day with the same result.
I have the 16gb version with the games installed on a usb drive formatted as internal space. Could that be the culprit?
I played through FF4 on my Shield TV just last year. Worked flawlessly. Still have FF3, 4, 5, 6, and 9 all installed and all launch without issues on my Pro. So it may indeed be using a USB drive causing that issue for you.