Why does GPP advocate the "snaking" pushup? 

One of the problems with most of the professional exercising world is their refusal to see benefit in a movement that isn't related to the original intention of that movement. 

For example.  Many exercise professionals cannot see ANY other reason to do biceps curls, other than to build very large biceps.  Classically, building very large biceps has to be done with strict form.  However, by swinging a biceps curl, you can work other parts of the body.  Yes, this will take somewhat away from the goal (if you had it) of building massive biceps, but it will add health and fitness to other regions and systems.  Namely your core and nervous system. It does this in ways which are hard to simulate.  In other words, there are no other moves we can use (situps, legups, etc.,) which can work these regions and systems as effectively as swinging a biceps curl. 

Once you realize this, it makes swinging a biceps curl - suddenly very cool!   

Back to our original point about snaking pushups.  What the greater exercising world generally misses is the fact that most exercises can be altered from their original forms to yield other healthy benefits to the user.  These benefits are every bit as important (more-so in many cases) to your health as the intention of the original exercise.     

Snaking pushups yield benefits to the entire body (core, nervous system, endurance) that strict pushups can't - for most people.  This mandates our use of them.