The recording sounds a bit off. (Let's leave aside the messed up यह for now.) Somehow, the cadence of the voice on है sounds weird.
Assuming that were "fixed": There are some little ways to hear the difference.
नहीं है : 1) In well-spoken Hindi it will have a clear "H" pronounced; 2) The है will often be dropped; 3) There is more of an emphasis on the second syllable of नहीं, whereas in नयी it is more on the first syllable.