Alas, iOS 4.2.1 is the newest one for that device. However, there is a way to find compatible games and other apps, so don't despair!
Find Old Apps for iOS [ http://findoldapps.com/ ] lets you search the App Store for older iPod apps by country; filter by iOS version, device type, or category; and search by a free-form text field. You can also sort by rating, app name, category, year it was last updated, and price. It uses Apple's iTunes API to interface with the iTunes databases so that the site can find the apps for which you are searching.
To find games and apps compatible with your iPod, use the drop-down menus on the left of that Web site to select your iOS (4.2.1) and your device (iPod touch 2nd gen.). After that, select the options you want to find the apps for you! Be aware that some of them might not be available for download anymore, but most of those apps from the listings shall still be on the App Store.
Note: I am not affiliated with that Web site nor its author, but I spent far too long searching the Internet before I found his site once again after months of forgetting its name and Web address and yearning to find it. I'm going to make sure others and myself don't have to search nearly as much in the future by posting a link to it here alongside a description.