Most likely you need to be working at a larger scale for that. Edges too short for SketchUp to form them. You can see some missing faces after the Intersect at the top of the miter. That’s typical when edges get too short, too. Scale it up by a factor of 100 or maybe 1000 before doing the intersection. Better, use the Dave Method.
Don’t forget to erase that short little line segment sticking up at the back corner, too.