What does it mean for it to be a 64k demo. That all the code required to produce the video fits in 64k? Can they call external libraries? How do they talk to graphics hardware?
The executable file may not exceed 65536 bytes. No external data files are allowed. Any and all external libraries available on the compo machine may be used, including OpenGL/DirectX. The full specs of the compo machine, including software configuration are announced beforehand. In general, you can pretty much expect a stock win7 machine with modern hardware.
In 64k competition, data such as textures, models, samples/synth, etc. are either precomputed or generated on the fly. Most groups have their own tools or use tools available in the community.
They need to produce an .exe below 64kb in size that can run on clean versions of Windows and display the demo. That 64kb includes everything (textures, models, music, code etc). I think most modern demos use DirectX.
Edit: Second place is a 64k demo: http://www.youtube.com/watch?v=69Xjc7eklxE