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.
Which leads to the common trick: If a train is delayed, it will often skip the last stop and turn at a station before the last. So the train was cancelled and not late at the final destination, therefore doesn't affect the punctuality statistics.
And yes, in Germany this happens and is reflected in rising "cancelled train" statistics. KPIs for Deutsche Bahn managers haven't caught up yet ;)
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.