Its not exactly that the engine is utilised in a different way, more like the engine is not the same. When you write a game engine, most of the work is low level stuff - invoking system and graphical libraries. All this low level stuff has to be rewritten becouse the API is different. The most obvious and important difference is the graphical library - windows games usually use DirectX that is unavailable on other systems and thus has to be replaced with OpenGL. This is almost like writing the engine from scratch, but with one difference - when you do something the second time you learn from the mistakes and do it better. Additionally, IMHO, the linux API makes more sense, which helps in creating better solutions. They also didn't do it in a hurry like relic and that always makes a huge difference in coding - you simply have time to think of optimisations.
You also should keep in mind that everything is different between linux and windows. Nvidia makes separate drivers. Processes are scheduled in a different way. There is a different utilisation of memory and disk. Generally linux is more lightweight and doesn't spend its resources on so much user-independent stuff that slows the computer down.
All of these factors contribute to linux often being more performant than windows. But honestly I don't know which one contributes the most, that would need some really extensive testing (or googling )
Cool! Thanks for the explanation man! I never understood this completely!