As I read it, the alternative implementation should branch of at a single point in the code. The alternative path usually requires modifications in the functions and data it's calling and using. But instead of going through the code adding flags everywhere, the idea is to make a source code copy and modify that. It duplicates source code, but keeps the original implementation untouched.
I can imagine that it allows more freedom re-working the code. You don't have to worry about breaking the original implementation this way, freeing up mental capacity.
another way he seems to have found to free mental capacity - his text is suspiciously lacking mentioning of abstractions and design patterns. Switching between implementations? There is a pattern for that!
Yeah - if only Carmack had read the Gang of Four on http://en.wikipedia.org/wiki/Design_Patterns - imagine how much more he would have accomplished! He could have used the Flyweight pattern for texels, since the same color is used many times - and that's just one example! :)
I can imagine that it allows more freedom re-working the code. You don't have to worry about breaking the original implementation this way, freeing up mental capacity.