It is not entirely correct that "[s]ales from stock traded on established securities markets" are exempt from tax.  And there is no such thing in the tax code as "Publically traded exemption" (with or without the correct spelling).

Fundamental to your question is where your client's tax home is, assuming this is not US-ECI but FDAP.  Just because an individual is classified as an NRA does not automatically translate to the individual not having a tax home in the US.  Those are governed by two separate section of the IRC and the Code section that determines the sourcing of the gain is predicated on whether the individual has a tax home in the US.  Taxpayers who is in the US for 183 days or more would have US-source capital gain subject to tax at 30%.

Page 4 of 1040-NR is only for US-source FDAP.  If you enter that on this page, PS will treat that as US-source and apply the 30% tax mentioned above.  If the gain is not US-source because your client was an NRA who did not have a tax home in the US (remember one does not always equate to the other), the gain is simply not reportable.  You will need to notate that separately on the return but still claim a credit for the tax withholding.

To file a refund claim on a 2019 1040-NR, your client should apply for an ITIN and attach the 1042S with tax withholding to the return.

Your client should also file the W8-BEN asap to avoid this from recurring in 2020 (which is almost half-way through - believe it or not).