I believe Aberforth was referring to the picture with Bill Weasley and the dragon in which the goblins are firing spells/sparks at the dragon, not the one with the single goblin in front of the row of doors.
I see a few ways this could fit the fiction:
1. They may have some previously unmentioned devices that fire sparks or stinging jinxes or whatever.
2. If the guards are down for the count, they could have grabbed up their wands, though I'm not sure they would be able to use them right away
like that. The books suggest it's not impossible for goblins to use wands, it's just outlawed.
3. Goblins do possess their own type of wandless magic, but it's not described in any real detail. I don't know if it would give them the ability to fire
spells directly out of their bare hands, but it's possible.
http://harrypotter.wikia.com/wiki/Goblin_magic