Angry Birds is a "me too" product in its own right, with its mechanics copied from popular flash games like Crush the Castle. Where it differentiates is its polish and style, as well as widely accessible characters, and a dedication to releasing new content.
It also wasn't an overnight success. It released in December 2009 and dropped off of the top paid app charts in the US without making much of a splash, and only began its meteoric rise months later after an update with more content and a lucrative negotiation for a "Game of the Week" iTunes feature from Apple.
Angry Birds is the maker's 52nd game. Overnight that.