Since graphic designers/end users are not programmers, what are the technique to allow them to add new tasks or change application logic in a game? what are the end user tools? I want some popular examples.
Various scripting languages, both text-based (ones with simple syntax - LUA for example - can be more accessible for a non-programmer), and graphical (Unreal, for example, is very GUI oriented).
Alternatively I've seen people just expose tweakable stuff through an editable text file (sometimes a CSV formatted file usable in Excel), if you expose the right stuff you can give designers fairly powerful abilities to change the game, without them having to actually alter the logic.
Basically the tools I've seen being used are:
Unity is a very popular engine/WYSIWYG editor which allows programmers to expose easy to modify "components" which artists/designers can attach to entities to give functionality within the game. A bunch of components come standard which provide a lot of the basic functionality for games.
From the Unity site: