Yo have a 2G iPod.
iPod touch (3rd generation) features a 3.5-inch (diagonal) widescreen multi-touch display and 32 GB or 64 GB flash drive. You can browse the web with Safari and watch YouTube videos with Wi-Fi. You can also search, preview, and buy songs from the iTunes Wi-Fi Music Store on iPod touch.
The iPod touch (3rd generation) can be distinguished from iPod touch (2nd generation) by looking at the back of the device. In the text below the engraving, look for the model number. iPod touch (2nd generation) is model A1288, and iPod touch (3rd generation) is model A1318.
The description for the app in the Apple App store says:
Compatibility: Requires iOS 5.0 or later. Compatible with iPhone, iPad, and iPod touch. This app is optimized for iPhone 5.
Thus, either get a newer model iPod or try to get a refund from Apple.