If the aircraft is still able to take off with full fuel/pax on a short runway it shouldn't affect the range very much, should it?
That is true. But if the runway is too short to take off with full fuel and all of the pax, then we need to carry a reduced fuel load (or really annoy some of the pax by leaving them behind). This reduced fuel load will reduce our range.
We could also argue that short runways will prevent us from doing reduced thrust (assumed temperature) take-offs and this will increase the fuel used in getting off the ground. This might reduce range by a small amount.
But the problems really begin when the runway is so short that we are obliged to carry a reduced fuel load.