Caveat - I've not played minecraft - but I suspect that the graphics are not the problem, but the simulation (the atomically destructible environment and also AI).
Modern 3d games involve using both the CPU and GPU, and most intensive graphic computation is done on the GPU.
Graphical elements like having complex models, shader effects, filter passes etc. all put strain on the GPU, but don't touch the CPU too much.
Game logic elements like destructible terrain, AI, pathfinding, physics, and generally extensive game rules all put strain on the CPU.
Different games have a different balance between the two (but eventual framerate and performance is determined by the slowest side), a highly detailed FPS (say, Halo) is likely to be GPU-bound, whilst a complex strategy or simulation (eg. Minecraft) is more likely to be CPU-bound.
