No, thrust to weight ratio difference is not enough to make up for the lack of lift, because your acceleration on the runway is still limited due to practical reasons. You need greater lift at higher altitude airfields in tropical areas to take off with the same load, and the F-16 does not make the grade due to its higher wing loading.
Think of it this way: The bulk of what is lifting the aircraft at takeoff is coming from the wing area. The maximum speed that the F-16 and the Mirage 2000 can achieve on that runway is limited by practical reasons (like friction on the ground as well as runway length), and hence will be about the same. Thus for the same speed, the greater Mirage 2000 wing area will generate a greater amount of lift, thus allowing the Mirage 2000 to take off with a greater load. These things matter more at the higher altitude airfields in the tropical, thinner air of India during the summer. Thrust to weight ratio does not make as much difference due to practical reasons like friction between tires and the ground when taking off.