> Can you please elaborate, the first part of the sentence says graviton is for non-self-interacting gravity, the second part of the sentence says graviton is for self-interacting (if 'its' in 'its self-interaction' refers to the graviton).

The point is, we know gravitation does self-interact. But our best model, the graviton, doesn't model self-interaction. So the model is probably accurate in regimes where you'd expect little self-interaction anyways.