Your best bet for a legally grey but functional route is to find a copy of Angry Birds Rio from eBay or thrift stores. Some of these disks were manufactured with an offline activation bypass or came with a pre-filled key that works despite the server shutdown. Look for the "Noviy Disk" publisher versions (common in Eastern Europe).
Version 1.4.4 was a massive milestone for the game, featuring: and Market Mayhem episodes. Hidden golden beachballs and fruit to find. angry birds rio activation key for pc version 1.4 4