How can I get Angry Birds on my Mac?
The App Store found in iTunes is only for iPhone/iPod/iPad apps. Mac apps can be found on the Mac App Store. Angry Birds is available for Mac for $5.
You can also play for free online at http://chrome.angrybirds.com/.

Note that iPhone and iPad apps are not linked to desktop Mac apps, so when you buy an app for an iPhone or iPad, it does not come with a Mac version and there is no guarantee that a Mac version is even available.
Sometimes apps are available on both the iOS (iPhone/iPad) App Store and the separate Mac App Store, as is the case for Angry Birds.