Running the ball has been a buzz topic surrounding Griffin during his first two NFL seasons. His feet made him electric during his rookie year. This year, the hits he took were viewed as senseless.
It would be a surprise to nix RGIII's running skills completely. NFL teams don't get into the habit of removing an arrow from a player's quiver.
However, there is a good chance that under Gruden, the running plays for the quarterback could be heavily de-emphasized. That is not to say they would go away completely. Gruden ran some effective read option with Andy Dalton in Cincinnati, so the coach certainly finds it a worthy change-up.
It's clear that Griffin understands his future in the NFL is dictated by his improvement in the pocket. He can still be a scrambling threat without a plethora of read-option plays.
RGIII's legs make him a dynamic player, but his arm makes him a quarterback. He understands becoming a precision passer will elevate him and the team's new offense.