Can two dimensional shapes be classified as polygons?

YES!!!

Polygons are all 2-dimensional shapes.

Compare to

Polyhedrons are all 3-dimensional solids.

'poly' means ; Many

'gons' 2-dimensional

'hedrons 3-dimensional

So a polygon is a 2-dimensional shape of any number of sides.

A polyhedron is a 3-dimensional solid of any number of faces.