He might not have been aware of the full extent of the damage. He is on final; the plane is flying; he's lost an engine; he's going to land it. There is no time for anything else.
This is likely true. He was the only person onboard the plane, so he would not have been able to get up and look. Unlikely he could see the extent of damage from his seat. And as noted, on final approach, he doesn't have time for much to change plans. Even if he knew the extent of the damage, the choices are roughly the same - land as planned, or go around.
That said, he did exactly what he should. Aviate, navigate, communicate. He controlled the plane, made a decision, and communicated that to ATC. Well done.
Most multi-engine airplanes can even take-off and climb with only a single engine functioning. You would never do it intentionally, but sometimes engines fail shortly after takeoff when you are 50 feet above the runway.