I think they just wanted to steal the plane, to use it for some mission later on. The 777 costs about $300 million US. It can fly more than halfway around the world without refueling. If it can carry several hundred passengers, then it can carry instead lots of cargo (weapons etc.).
Now, let's use our imaginations and pretend WE want to steal this plane. How would we go about it? How would we gain access to it - and how would we get it off the ground? Pretty much any runway long enough would be controlled by a tower. And we'd want to steal it with the fuel tanks full. So really the best/easiest time to steal it is when it has been fueled up, thoroughly checked by the ground crew, and cleared for takeoff as a scheduled flight. Airport security has checked the passengers to make sure none of them have weapons or anything that could interfere with our mission to steal the plane.
So, we take off. Once we get outside of our departure airport's airspace, that controller no longer needs to talk with us. Typically at this point the controller will tell the pilot to change to a different frequency so that he can talk to the controller for the next airspace he is entering. In other words, one controller "hands you off" or "hands you over" to the next one. It's sort of like when you're on the phone and the person tells you they're going to transfer you to another department. Sometimes there's a pause before you're connected with the next department. So with the airliner, this hand off would be a good time for us to shut off the communication equipment. Controller #1 has "hung up his phone" so to speak and controller #2 is waiting for us for start talking. Now, if we drop off the radar they're going to assume we're going DOWN. So let's fool them and go UP. Way up, higher than where normal flight activity takes place, as high as we can get this plane to climb. OK we got up here, now the passengers might start to get suspicious so let's put on our oxygen masks and quickly immobilize the passengers by depressurizing the cabin just enough to deprive the passengers of oxygen. This way, they will all get drowsy and then pass out within seconds. There! Now none of them can make phone calls or send text messages. In another minute or so they will all painlessly and silently die from lack of oxygen. Now we just have to keep evading the radar - possibly with the help of other terrorists who are in other aircraft scrambling signals - and we're on our way to our destination. Upon arrivial we'll just despose of the dead passengs, and we have ourselves a nice big plane to use as we wish. It is not unusual for controllers to ask other airborne planes to be on the lookout for a lost or unresponsive aircraft. Good thing those other pilots are our fellow terrorists! As they wave to us from their cockpit they tell air traffic control they do not see anything.