I do not believe so. But the DCs of those abilities would increase with advancement. You could always increase them if you feel it is appropriate but I don't think there are rules that cover it.
If you want to you can just apply the increased damage chart to all abilities. I just haven't seen a rule that says you should do so. You are right many of the monsters seem to use some sort of damage scaling for their other abilities. So I think it would be reasonable if you wanted to do it. The rules do say "A size increase affects any special ability the creature has that is affected by size". So if you think a special ability would be affected by the size increase then I think you have at least tacit support from the rules.