According to SE its a ranged attack, just like Jump :> The distance closing ability is an "added effect" of the ability. Just like how Spinshatter Dive does the same thing; but vanilla Jump doesn't. DRG has 4 ranged attacks. MNK has 1. PLD has 2. WAR has 1 native.

Shoulder Tackle was specially made like it is so Monk WOULD have a Ranged Attack in ARR, thus it is one.