The ability triggers only once, no matter how many creatures are blocking it. The ability resolves and deals damage to those creatures before combat damage is dealt. Even if that damage destroys all creatures blocking Battle-Scarred Goblin, Battle-Scarred Goblin doesn't become unblocked.
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.