Despite what the article says, a creature with the special ability improved grabimproved grab does not also have the unique ability to simultaneously drag away a grappled foe
As mentioned, the Monster Manual (even the most recent 2012 premium edition) includes in the special ability improved grabimproved grab a section saying that
Emphasis mine. That a creature can move after having grappled another creature is true as per the Player's Handbook rules on grapplegrapple, but
Just in case this is worrisome, there are at least two other places wherein similar unplayable rules persist in the text. I know that it's really difficult to let go of such troublesome artifacts, but the system isn't perfect, and letting some things go is okay. (See this question about the spell major imagemajor image and this question about accidentally activating magic items.)
On those Rules of the GameRules of the Game columns...
That's cool. From Sandstorm the general feat Scorpion's Grasp mimics much of the special ability improved grab, including giving the DM specific rules he can choose to use if he wants to implement the It can even move sentence as originally presented in the special ability improved grabimproved grab:
Were I a player, however, I would want the DM to make such house rules clear before, for example, being attacked by an ankhegankheg (which can, in the same turn, make such an off-hand grapple then burrowburrow away, my character in its mandibles).1