Well, remember that without the word "choose," there is no actual target for the effect.
Seriously, though, when determining what an effect is working on directly, you always look to the subject of the sentence. So, yes, since the effect is worded "character abilities cannot be triggered," this event works directly on character abilities. If it were phrased as "players cannot trigger character abilities," it would be considered to work directly on players. If it were phrased as "characters cannot trigger their abilities," it would be considered to work directly on the characters.
If it helps, think of this event adding a play restriction to all character abilities that says "this ability cannot be triggered this phase."