This incident never came close to being as bad as the Tenerife crash because the Lufthansa crew could see the EgyptAir plane and they aborted their takeoff early enough to stop.
I think they slammed the brakes when told to cancel by the controller, not because they saw Egypt Air on the runway. The latter may well have been too late. So, it's probably the controller to be credited first - and the fact that he could see the conflict (window or ground radar). Of course, Lufthansa's response was also good either way.
When listening to the audio, the first officer immediately replies to the tower that they're rejecting the takeoff. He wouldn't have done that if they weren't already slowing down. Plus, the Lufthansa had the best view of what was happening, if the tower could see that EgyptAir had missed the turn then the Lufthansa pilots could certainly see a 777 heading onto the runway in front of them.