The same teaching was infallibly defined by a subsequent Ecumenical Council:
“And since it arises from the necessity of salvation that all the faithful of Christ are to be subject to the Roman Pontiff, just as we are taught by the testimony of the divine Scriptures and of the holy Fathers, and as is declared by the Constitution of Pope Boniface VIII of happy memory, which begins ‘Unam Sanctam,’ for the salvation of the souls of the same faithful, and by the supreme authority of the Roman pontiff and of this holy See, and by the unity and power of the Church, his spouse, the same Constitution, being approved by the sacred Council, we renew and approve.”
(Pope Leo X, Fifth Lateran Council, Session 11, 19 December 1516)
So it is infallible. The subjection of the faithful to the Pope is a necessary part of the plan of salvation, just as all seven Sacraments are a necessary part of that plan. However, this does not imply that non-Catholics cannot be saved. They can be saved by being members of the Church non-formally, in other words by a mystical membership in the Church, even if they outwardly reject Her.
Fourth Lateran Council: “There is indeed one universal church of the faithful, outside of which nobody at all is saved, in which Jesus Christ is both priest and sacrifice.”
Pope John Paul II: “Since Christ brings about salvation through his Mystical Body, which is the Church, the way of salvation is connected essentially with the Church. The axiom ‘extra ecclesiam nulla salus’ – ‘outside the Church there is no salvation’ – stated by St. Cyprian (Epist. 73, 21; PL 1123 AB), belongs to the Christian tradition. It was included in the Fourth Lateran Council (DS 802), in the Bull ‘Unam Sanctam’ of Boniface VIII (DS 870) and the Council of Florence (Decretum pro Jacobitis, DS 1351). The axiom means that for those who are not ignorant of the fact that the Church has been established as necessary by God through Jesus Christ, there is an obligation to enter the Church and remain in her in order to attain salvation (cf. LG 14). For those, however, who have not received the Gospel proclamation, as I wrote in the Encyclical ‘Redemptoris Missio,’ salvation is accessible in mysterious ways, inasmuch as divine grace is granted to them by virtue of Christ’s redeeming sacrifice, without external membership in the Church, but nonetheless always in relation to her (cf. Redemptoris Missio, n. 10). It is a mysterious relationship. It is mysterious for those who receive the grace, because they do not know the Church and sometimes even outwardly reject her. It is also mysterious in itself, because it is linked to the saving mystery of grace, which includes an essential reference to the Church the Savior founded. In order to take effect, saving grace requires acceptance, cooperation, a ‘yes’ to the divine gift. This acceptance is, at least implicitly, oriented to Christ and the Church. Thus it can also be said that ‘sine ecclesia nulla salus’ – ‘without the Church there is no salvation.’ Belonging to the Church, the Mystical Body of Christ, however implicitly and indeed mysteriously, is an essential condition for salvation.” (All Salvation Comes through Christ, General Audience, 31 May 1995.)