"taking the re-projected z value as the keypoints' depth D{ij}" is actually not what this paper does.
I means "re-project" might not be the right word for this operation.
It actually convets 3D keypoints from world coordinates to camera coordinates. And then taking the z value as the depth D{ij}.
Your understanding is correct -- By "re-project", we mean converting 3D keypoints from world coordinates to camera coordinates and taking the z values as depths.
"taking the re-projected z value as the keypoints' depth D{ij}" is actually not what this paper does. I means "re-project" might not be the right word for this operation. It actually convets 3D keypoints from world coordinates to camera coordinates. And then taking the z value as the depth D{ij}.