Do -1/-1 counters count as damage?
In general, -1/-1 counters do not count as damage. However, in the case where an ability (such as Wither or Infect) says that damage is dealt in the form of -1/-1 counters, it does count as damage. When a creature with one of those abilities deals damage to another creature, it still counts as dealing damage to the other creature, but instead of marking damage, you put that many -1/-1 counters on the other creature.

This means that damage dealt by a creature with Wither or Infect would trigger Rite of Passage.