Sorry, but that article is inaccurate. We've asked several times for it to be corrected to make it more clear, since a 2nd-generation iPod touch cannot run iOS 4.3 or later, but as yet no corrections have been made.
Your iPod should support AirPlay, since that was introduced in iOS 4.2, but only with the built-in apps. To stream any third-party apps requires iOS 4.3 which will not run on your iPod. That's probably what's being referenced in the article, but it's certainly confusing.
By the way, you posted in the iPad forum. For help with an iPod touch, it's usually best to post in the forum for that device.
When you talk about built-in apps, you mean the Apple "music app", and not the Apple "remote app" or any third party, right? If so, how to you stream from the "music app"? I can't seem to find any airplay button or functionality on that app.
This is on iOS 4.2.1 on iPod touch 2nd gen.
Correct, just the Music app. If you don't see an AirPlay button, then the iPod probaby doesn't find a device to connect to. I presume you have a 2nd or 3rd-generation Apple TV or Airport Express? If so, this may help: