If I buy Angry Birds on iPad and iPhone, do I have to buy it again on the Mac App Store?
I don't have a source, but the thing is that the iPad/iPhone AppStore is different than the Mac Apple Store. The iPhone game costs 0.99, whereas the iPad version (optimized for the larger screen) is more expensive, yet these two apps are in the same Store.

Since there's no way (thanks the Apple) to provide free upgrades to the Mac Apple Store for existing customers, Rovio charges you for the game again if you want it in your Mac, no matter how easy it was to port for them. 

It was probably not a super hard task, but in terms of administrative work, they have no choice unless they'd wanted to give it away for free, which clearly they aren't. 

So the answer is yes, you have to buy it again from the Mac Apple Store.