The difference between a Jewish or Christian wife and a wife who does not pray

There is no mistake in the fatwa referred to. Rather the mistake comes from the questioner wanting to regard as equal a woman who is supposedly Muslim but does not pray and a woman who is Jewish or Christian, on the basis that neither of them prays. 

This regarding them as equal is not valid, because there is a difference between them, which is that not praying is major kufr and apostasy that puts a person beyond the pale of Islam. This has been explained in many answers on this site, such as the answers to questions no. 9400 and 5208. 

Based on this, the woman who does not pray is a kaafir and an apostate from Islam. 

The ruling on one who has apostatized from Islam is more severe than the ruling on a Jew or Christian. 

Shaykh al-Islam Ibn Taymiyah said: 

The apostate is worse than a kaafir in many ways. End quote. 

Majmoo’ al-Fataawa, 2/193 

Hence meat slaughtered by an apostate cannot be eaten, whereas meat slaughtered by a Jew or Christian may be eaten. It is not permissible for a Muslim to marry an apostate woman, and if his wife apostatizes, the marriage contract becomes null and void, but it is permissible for a Muslim to marry a Jewish or Christian woman. 

The crux of the matter is the ruling that one who does not pray is a kaafir. Those who are of this view forbade marriage to a woman who does not pray, and said that it is obligatory to leave a woman if she stops praying. This is the view of Imam Ahmad (may Allaah have mercy on him) and was stated in fatwas by a number of scholars, such as Shaykh Ibn Baaz (may Allaah have mercy on him), Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) and Shaykh Saalih al-Fawzaan (may Allaah preserve him). Our fatwa on this issue and similar issues is based on their fatwas.  

Similarly, if a woman does something that implies kufr, such as vilifying Allaah, may He be exalted, or vilifying His Messenger (peace and blessings of Allaah be upon him), and she persists in her kufr and does not repent, then it is not permissible for her to remain the wife of a Muslim. The same applies if a husband is ruled to be an apostate, then he and his wife must be separated. 

And Allaah knows best.