To try the demos, you can download an archive. Each application explores different programming concepts (data structures, algorithms, modelization, etc.). Studying those examples should help you transform your ideas into working programs.
Building a chess engine is a non-trivial task. Each part must be rigorously tested and optimized: board representation, move generation, evaluation, search. Furthermore, the amount of memory needed during a search is extremely variable. Since building a strong engine is pointless (there are many really strong open source programs), the focus will be on creating a tool that can help a human player analyze a position and make sense of it. A collection of World Championship games will be available for study.
minimax, alpha-beta pruning
The shoooter is more or less a performance test of the logiqub. Thousands of sprites animated on screen.
sprite animation, background scrolling, memory pool, collision detection, trigonometry, timed events
sprite animation, RGB color model
autonomous agent, pathfinding
random number generator
A visual interpreter to see step by step what happens inside a stack virtual machine. It's an amusing concept to build an interpreter on top of another. There is also an user interface automaton to reproduce a sequence of button presses.