Thank you for the files. Very much appreciated!
With v1.0.1 the dl.bin isn't needed anymore, as it will be generated automatically by the game on the first run. A data connection is not needed.
So the installation steps are even easier now:
1. Install
patched Google Play Store v3.10.10 by ChelpuS & SaNXeVC or use
Google Play Store v3.10.10+Installer v1.0.5 by ChelpuS (probably easier for most people)
2. Install FINAL FANTASY DIMENSIONS v1.0.1 APK
3. Copy main.101.com.square_enix.android_googleplay.ffl_gp.obb to /sdcard/Android/obb/com.square_enix.android_googleplay.ffl_gp
4. Play!
I looked around a bit, but I couldn't find any reports about compatibility issues with your device, the Samsung Galaxy Ace.
Can your run any other games, i.e. FINAL FANTASY III?
And yes, also try to clean the game from your device, as suggested by UndeadSquirrel and Rewdboy05.
Look for the folder
com.square_enix.android_googleplay.ffl_gp in
/data/data,
/sdcard/Android/data AND
/sdcard/Android/obb.
Also I didn't find the dl.bin in your TB data so I guess your game instlalation couldn't connect properly or verify its license with the Google Play Store in the first place, so it really seems that it's just a bad installation caused by some leftovers from the TB data in the first post.
As a last resort you could try another ROM.
Let us know how it goes!