Why does the Catholic Church say that the plan of salvation includes Muslims?

(OP) Firstly, this seems to imply that Muslims worship the same God as the Christian God; secondly, perhaps a corollary of the first point, it suggests that Muslims are also given salvation.

The idea underlying the belief that all who worship God, but who do not acknowledge His Son or God the Father (Trinity), including Jews, Muslims, and others is recognizing the common source of these religions. To take it a step further back in time, it is recognizing all peoples source to Noah and the metaphor of his ark. To bring it forward under the term Christian, it is the recognition of a common Christian (Trinity) baptism (though a different question).

Nearly everyone recognizes the difference in faiths, but the Catholic Church believes the common denominator (Abraham) is the unifying factor.

The Church and non-Christians

[839] "Those who have not yet received the Gospel are related to the People of God in various ways."³²⁵

The relationship of the Church with the Jewish People. When she delves into her own mystery, the Church, the People of God in the New Covenant, discovers her link with the Jewish People,³²⁶ "the first to hear the Word of God."³²⁷ The Jewish faith, unlike other non-Christian religions, is already a response to God's revelation in the Old Covenant. To the Jews "belong the sonship, the glory, the covenants, the giving of the law, the worship, and the promises; to them belong the patriarchs, and of their race, according to the flesh, is the Christ",³²⁸ "for the gifts and the call of God are irrevocable."³²⁹

[840] And when one considers the future, God's People of the Old Covenant and the new People of God tend towards similar goals: expectation of the coming (or the return) of the Messiah. But one awaits the return of the Messiah who died and rose from the dead and is recognized as Lord and Son of God; the other awaits the coming of a Messiah, whose features remain hidden till the end of time; and the latter waiting is accompanied by the drama of not knowing or of misunderstanding Christ Jesus.

[841] The Church's relationship with the Muslims. "The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind's judge on the last day."³³⁰

[842] The Church's bond with non-Christian religions is in the first place the common origin and end of the human race:

All nations form but one community. This is so because all stem from the one stock which God created to people the entire earth, and also because all share a common destiny, namely God. His providence, evident goodness, and saving designs extend to all against the day when the elect are gathered together in the holy city...³³¹

Catechism of the Catholic Church (bold added, italics in original)

But what about the Catholic papal bull Unam Sanctam (1302) teaching that in order to be saved you must be subject to the Roman Pontiff? We read further in the Catechism:

"Outside the Church there is no salvation"

[846] How are we to understand this affirmation, often repeated by the Church Fathers?³³⁵ Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:

Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.³³⁶

[847] This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:

Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience - those too may achieve eternal salvation.³³⁷

[848] "Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men."³³⁸

-ibid-

In other words, if one does not know Christ or His Catholic Church, but yet seek God, as do Muslims, Jews, and others, they believe they may be saved. Perhaps it is in purgatory. Perhaps some other way like earned, paid for, God's grace, or otherwise.

To answer the OP, while I am not of the Catholic Church, nor do I speak for the Vatican, one may use source documents to the best of one's abilities; it (Catholic Church) would say because they (Jews and Muslims) share the same origins as Christians (Abraham), and believe in that original commonality, they believe those outside the Catholic Church may be saved in mysterious ways.

PS. If I have missed a point, please let me know.