“How come some apps I download from the App Store doesn’t fill the whole screen on my iPad?”
Some apps for the iPod touch and iPhone can be used on the iPad, although the app may not take advantage of the bigger screen on the iPad.
If you download a game that was only created for the iPhone/iPod, you can tap on the ‘2X’ icon on the app to enlarge it. This will zoom in on the app to fill the whole screen on the iPad.
If you don’t mind looking at a pixelated app this is a quick fix. There could be an iPad optimized or universal version of that app, double-check the App Store.