Can a polygon be one dimensional?

Your set of vertices satisfies all the terms of the definition, so it is technically a polygon by that definition. Some would call it a degenerate polygon.

To disallow degenerate polygons, you will need to modify the definition, adding additional constraints.

EDIT: in the original post, I claimed that adding the condition that there exist at least non-collinear segments would remove the degenerate polygons. This is false: see comments.

These things are not universally defined. In some contexts it would make sense to admit your example as a polygon, and in others it would not.

An example of the first context would be a discussion of a computer algorithm for detecting whether a point was interior to the polygon, or for calculating the area or the convex hull of a polygon. One would expect the algorithm to work reasonably even for a degenerate polygon.

An example of the second context would be the study of plane tilings or tessellations, where degenerate polygons are uninteresting as tiles, or a discussion of the triangulation of manifolds into simplices, where the triangles are expressly required to be non-degenerate.

Typically (but not always) each author will state the particular definition or at least make a remark like “we exclude degenerate polygons”.