Continue to grill with the lid open for about 4 - 6 minutes. Flip the steaks over onto the other side, still over the hottest part of the grill. Grill the rib eye steaks for an additional 4 - 6 minutes on the other side, lid open, for a medium-rare delicious steak.Remove the steaks from the grill and allow to rest for 5 minutes before serving.The resting period is important so that the juices don't run out when you cut into the ribeye, so be patient!lip the steaks over onto the other side, still over the hottest part of the grill. Grill the rib eye steaks for an additional 4 - 6 minutes on the other side, lid open, for a medium-rare delicious steak.