The article writer is not misleading you. Although you can still use airplay through iTunes to send movie playback to your ATV, mirroring your display has been so far limited to only newer hardware configurations only. Even on Apple's technical specifications page for Mountain Lion this is documented.
On this page:
Apple - OS X Mountain Lion - Read the technical specifications.
in the feature specific requirements section you will find:
AirPlay Mirroring
Requires a second-generation Apple TV or later. Supports the following Mac models:
iMac (Mid 2011 or newer)
Mac mini (Mid 2011 or newer)
MacBook Air (Mid 2011 or newer)
MacBook Pro (Early 2011 or newer)
As you can see, 2011 or newer.
I know from personal experience, a 2010 MBA won't do airplay mirroring.
If your hardware doesn't support it, the option just doesn't show up to even enable the feature.
If the only reason you want ML is the airplay mirroring, then there is no reason to update.
If you want/need the functionality of Airplay but don't have a Mac capable of it - check out
AirParrot - AirPlay your Mac or PC's screen to AppleTV which works fairly well. I did use it a bit on that 2010 MBA for mirroring, didn't feel as smooth as ML airplay looks in demonstrations, but it does work and it does have a trial version.