Author here. The water effect is a simple 2D heightfield simulation, which is explained pretty well at http://www.matthiasmueller.info/talks/GDC2008.pdf. It essentially just moves each vertex toward the average height of its neighbors, which turns out to propagate waves that look like water ripples.

The caustics are also pretty simple. Basically you take your heightfield mesh that represents the water surface and project each vertex independently along the ray refracted from the light through that vertex (using the vertex normal) and onto the pool floor. So you now have a mesh that is completely on the pool floor and contains lots of tiny triangles. To render caustics, just make triangles that got smaller brighter and ones that got bigger dimmer. I think I used the ratio of the projected area to the original resting area.

The reflection and refraction raytracing is all hard-coded for the geometry in the scene, which makes it really easy. It's just a simple sphere and box intersection test. The "ambient occlusion" is done by making parts of the objects darker when they get near each other.

State of the art for real-time water uses a full 3D volumetric representation for the water like in this paper: http://www.matthiasmueller.info/publications/tallcells.pdf. This lets you get waves that can fold over themselves like real waves. I haven't seen any other realtime methods that have caustics as good as the ones in my demo though.