Distributing more than 50 full versions of my application I have an iOS application, and apparently I can have a max of 50 promo codes.

There is this kickstarter game: http://www.kickstarter.com/projects/293831888/pota-toss-amazing-indie-ios-game-with-gps-based-le

In the second reward tier, it says it will give a full version of the game for free. I see 98 backers.

How can they offer more than 50 full versions of their game? Do they use a method other than promo codes? Can someone request more promo codes?
You can achieve this by signing up for the iOS Developer Enterprise program. This will allow you unlimited ad-hoc builds of your application, which will mean that you can deploy unlimited copies of your .ipa to send to as many users as you want.