Why does the laser reflect like a semicircle?

Your description of rotating by 90 degrees doesn't make any sense. You show an image from one plaque "5th place" then talk about rotating 90 degrees and show an image from another plaque "4th place". It's not clear if this is meant to show the "90 degrees rotated" behavior or just that you see similar behavior for different plaques.

In any case what you are seeing is an example of specular reflection. The surface off which the light reflects is not perfectly flat so you don't get a direct reflection of the beam you send in, rather you get a distorted version. It is like a funhouse mirror.

Funhouse mirror

Notice how the curvature of the surface "stretches" the reflection in various directions depending on the direction of the curvature.

It is possible that the metal plaque off which the light is reflecting was polished (before engraving/labeling) using a circular polisher tool. This polishing might leave a very minimal circular pattern in the surface topography of the metal surface. When the laser beam hits this circular pattern it becomes distorted/stretched in the directions along the curvature of this pattern.

It is a bit difficult to say what exactly is going on without more information.