ipod zipklist app

Yes, the only way to get access to the internet with an iPod Touch is with WiFi. Or you can tether it to a cell phone, assuming you have the right software and a data plan.

Some stores have free WiFi, like Safeway and Target.

I agree. It doesn't look like this works offline.

I guess they're assuming you'll go to supermarkets that have free WiFi.

The descriptin says:

Seamlessly sync lists you create with lists on the web at www.ziplist.com. You can even sync up with most standard cell phones and other smartphones. No other shopping list tool allows such flexibility.

Than means to sync you need wifi/an internet connection.

From that decryption it also appears that you can use the app to purchase items without an internet connection. You just can't sync the list or use some other feature like barcode scanner.