MTG Question - Horobi, Death's Wail?

Can someone clear up for me, which creatures are exactly affected by Horobi's ability? It's said that creature that "becomes the target of a spell or ability", but according to the rules abilities are all most everything (flying, first strike, etc) , are creatures with those to be destroyed? Or, for example. would Deathbringer Thoctar be destroyed, when gaining additional +1\+1?