Why does contracting the iris allow less intense light to go in?

Imagine the iris like a shutter in front of a focussing lens (which, in fact, it is; see the diagram).

This means that any light going through the iris will be focussed on a very small point on the retina, and your eye is wonderfully developed in a way that this exact spot is the fovea, the only spot in the retina that allows you to see colour and high-resolution.

The iris does not modify the focussing function, it merely changes the amount of light going through into the lens to then be focussed onto the fovea. Imagine that every single object in your field of view reflects/radiates light in every possible direction - narrowing the shutter won't exclude parts of the field of vision, it will only exclude some of the rays coming in at very flat angles and thereby reduce intensity.

Only if your lens is deformed, focussing (adaptation) will malfunction (directing the gathered light to the wrong spot; or focussing the incoming light in front of or behind the retina) and blur your vision.