Usually the peripheral vision of human beings is weak, not stronger as that at the focused vision. It may not be normal for you to have the peripheral vision in dim light. I suggest you to go to have a check on the eyes fully in the hospital. You need to find the free time to do the check. It is very important.
Well, I need to say you are normal if it is not along with some painness. As we all know, we have two sorts of receptor cells, rod cells and cone cells. They function well so that we can distinguish color and shape of certain objects. I mean, rod cells locating at the periphery are capable to recognize the shape, while the cone cells setting in the center of the retina can identify the color. They are lowest at the edges and greatest at the center. The amount of receptor cells dominate the things we look at. So some people with more cone cells will see the things in front of them clearly and saliently, on the contrary, people with more rod cells are able to see things in dim light because the outline of a object need less chemical information to translate by our brain.
This phenomenon is quite normal. There are rod cells and cone cells on the retina at back of the eyes and opposite to the pupil. Cone cells are dominant in the center of the visual field and enable you to perceive colors. However, the cone cells in the bright light are not sensitive as in dim light. The rod cells are not sensitive to colors, but they are good for dim light and more competent in detecting movement. So when you are in an environment with dim light, your peripheral vision is better. If you want to see an object clearly in the darkness, you can use your peripheral vision by looking at it indirectly.