The original posting shows a particular situation with a very strong lateral light left of photographer and a deep shade on the other side, right of photographer.
If you point the dome toward the camera, the dome will collect light from both sides and "average" them. If you use the flat receptor and make two measurements and average them, you are going to have more or less the same results. No surprise in that.
The problem is that, in the specific condition of the picture of the original post, this "averaged" exposure might burn the highlights. When making an incident reading there is no explicit or implicit guarantee that the subject range will fall inside the dynamic range of the film. In a situation like this, where what we are interested in is the face of the subject, which is in the highlights, we want to avoid burning the highlights, and any "average" is a risky choice when using slides.
The point that was raised is whether, in the specific conditions of the picture of the original posting, wouldn't it be better to point the dome toward the light source, so as to be sure to have a reading which is appropriate for the girl's face, and letting the shadows fall where they may.
The dome will in any case collect light from its sides, so pointing the dome against the light source is going to give a slightly more open exposure than pointing the disk toward the light source. One can see it as an "average skewed on the highlights" which is IMO the most correct choice for that particular situation.