The correct view is that held by the majority: the prayer is valid, but he is sinful for abandoning an obligation. As for drawing an analogy with the first tashahhud, the obligatory takbirs, and the tasbih—such that whoever deliberately omits them without excuse has his prayer invalidated—this is an analogy with a relevant distinction. Congregational prayer is an obligation pertaining to the prayer, whereas the first tashahhud, saying samiʿa Allahu liman ḥamidah (Allah hears whoever praises Him), the takbir, and the tasbih are obligations within the prayer itself, more closely connected to it than an obligation pertaining to it.
HE MAY PERFORM IT IN HIS HOME …
His statement: “He may perform it in his home.”
“May” means: the individual.
“Perform it” means: perform the congregational prayer in his home; that is, it is permissible for him to pray in congregation in his home and not go to the mosque, even if he lives near it. Yet praying in the mosque is undoubtedly better. Thus, if he performs it in his home, it is permissible. If we hold that a congregation is established by two people, even if one of them is a female, this would entail that a man may pray at home with his wife and not attend the mosque.
This is what the author’s words imply. The proponents of this view cite as evidence the Prophet’s statement, peace and blessings be upon him: “The whole earth has been made for me a mosque and a means of purification.” (1) Thus, all the earth is a mosque. What is intended here is congregational prayer, and a congregation is attained even if a person is in his home, though it is better in the mosque.
Some scholars hold that performing it in the mosque is a collective obligation: if a sufficient number of people establish it, the obligation is waived for the rest, and those besides them may pray in congregation in their homes.