Q:

Definition of an intensive variable

The IUPAC definition of an intensive variable is:

Physical quantity whose magnitude is independent of the extent of the system.

Why is it defined for "a system", and not for a homogenous system, as for a heterogenous system the quantity (e.g. density, temperature) might be different for the different extents/parts of the system? 

A:

For a homogeneous material, an intensive variable is independent of the amount of material.  Even non-homogeneous materials approach homogeneity in each  small local region.  And in these regions, intensive variables have the same values as if you had if you had a large homogeneous region under the same local conditions.

