Perhaps this is just a projection of a square from a non-Euclidean space in which the lines are in fact straight and parallel.

I think the 2D surface of a cone (or double cone) would be an appropriate space, allowing you to construct this shape such that angles and distances around geodesics are conserved in both the space itself and the projected view.

This shape in that space would have four sides of equal length connected by four right angles AND the lines would be geodesics (straight lines) that are parallel.

No no no

Snack the keeps, booze the purge

That’s what they meant