I think its comical how Miami fan thinks they invented the wheel. Please go back and look at the 3 million times the Carolina Panthers ran the play you stole from them with DeAngelo Williams last year.
I didn't see the Carolina games in question, but there are many, many different formations where a direct snap to a non-quarterback is used. The Wildcat formation is one such and has a number of characteristic properties that distinguishes it from other direct-snap-to-a-RB formations.
That said, there are a variety of Wildcat formations as well. They're all double-wing formations, but if you look at the original one (Hugh Wyatt's, coach of a high school football team called the Wildcats), it actually has the quarterback lined up next to the running back, instead of wide. What the Dolphins are running is probably more correctly called the Wildhog, which was the variant introduced at Arkansas by Gus Malzahn (who had previously used it at Springdale High School). Malzahn was OC at Arkansas before (Dolphins QB coach) David Lee.
The Arkansas variant uses the unbalanced line, which is IMHO the reason Miami is having so much success with it.
I haven't seen any NFL team run anything closely resembling the Arkansas "Wildcat" package before this year, but I could be wrong (feel free to provide a specific game reference).
The original Wildcat formation:
http://www.coachwyatt.com/wildcat.html