What is it, exactly, that constitutes their "system"? I think HalfSmoke explained it before but you do a really good job of educating people on football. No snark, I'm being sincere here.
Several things. A strong zone running attack that thins out the defense at the point of attack in order to take advantage of the stretch play or a defense's over aggressiveness with cut backs. That's why Shanahan's system prefers offensive linemen to be extremely smart. They have to be able to read defenses, especially the interior linemen, in order to read on the run and get to the second level of the defense (Chris Chester was pretty good at that this past season). They prefer linemen that are athletic and not necessarily as big at the guard and center positions. The system is built to avoid negative plays so that even steady 2 or 3 yard gains will put the offense in favorable 3rd down positions. It's imperative that they avoid negative plays in order to have manageable distances on 3rd down. If you convert 3rd downs consistently in this offense it's almost inevitable that you will eventually gash the defense for longer chucks (maybe even a long TD) on the ground. At the same time, hesitation from defenses should leave them vulnerable to play action passes. Bootlegs are a staple of this system and can lead to huge plays when run correctly. That's why an athletic QB is preferred for this system. Luck could be really good at this but Griffin's athleticism could potentially cause nightmares for defenses. The intermediate passing game in this offense can be deadly if you have the right QB. As in every other offense the QB has to be a good decision maker (which is why I'm at a loss to explain how you were able to hang around for two seasons other than the fact that Jr loves to see you naked in the showers) and one who can push the pace. That's why Griffin seems almost ideal for this offense.