The answer to your question is "it depends". Some also do weighed calculations, where it's "per passenger", which means trains that have a high passenger load being late have a larger impact than one with few passengers. At least in Denmark, where I am most familiar (though I expect most of Europe to be similar), it's per stop.

As for the LIRR, it seems it's only the terminal station that counts:

> Thus, a train is considered late only if it arrives at its final destination six minutes or more after its scheduled arrival time.