It isn't to do with the length of the runway, it's to do with the size of the aircraft it's designed for.
For example, MEL RWY27 is relatively short, but still has a 74' PAPI.
Large aircraft (most wide bodies) generally aim at the 1500' (450m) markers to achieve the desired wheel height over the threshold (e.g. 35'). That is where a 74' PAPI is located.
A 53' PAPI is located at the 1000' (300m) markers, and is designed for smaller aircraft (up to narrow body jets e.g. B737/A320).