These applications can either be programmed individually, or you can build an abstraction that captures the common structure of a game. Reach supports typical programming language abstractions, like first-class functions (via arrow expressions) and objects, that can be used to build these abstractions.
When building such abstractions, the most difficult part is correctly capturing loop invariants of the user of the abstraction on the inside of the abstraction. Often, this means the abstraction must set up a protocol to communicate with its user, such as by receiving an invariant captured by an arrow expression.
See the abstraction workshop for a walkthrough of building such an abstraction.