Is there any game or gamified application for teaching/learning mathematics covering a high school/secondary school curriculum?
This is one major goal of Expii, a crowd-sourced work in progress.
Here are some other related projects I've seen:
- Alcumus from the Art of Problem Solving (AoPS): http://www.artofproblemsolving.com/Alcumus/index.php
- Brilliant: http://brilliant.org/
- Clever Math: https://www.clevermath.org/
- Curriki: http://www.curriki.org/
- DragonBox App: http://www.dragonboxapp.com/
- Euclid: The Game: http://euclidthegame.com/Tutorial/
- Established MOOCs like Khan Academy, Coursera, edX, etc.
- Oppia: https://www.oppia.org/
- Terry Tao's linear equation games: http://terrytao.wordpress.com/2012/04/18/new-version-of-algebra-game/
From what I can tell, Khan Academy currently seems like the "most comprehensive" answer to your question, but I don't know if it's what you're looking for.