As an evangelical protestant I am very glad to hear that. I had gotten the wrong impression by reading things that apparently are not true. If there is some other way to attain salvation besides faith in Jesus Christ, then He left His home with the Father and Holy Spirit in heaven, came into the world via the virgin birth, and died on a cruel Roman cross needlessly.
Now if the document would have added; "no man cometh to the Father but by me" I would be even gladder. But even so, the part of the verse that you quoted states the truth well enough.
(is gladder a real word?)
Here's what precedes the part you've hightlighted:
“The Catholic Church rejects nothing of what is true and holy in these religions. She has a high regard for the manner of life and conduct, the precepts and teachings, which, although differing in many ways from her own teaching, nonetheless often reflect a ray of that truth which enlightens all men”.
"...often reflect a ray of that truth....."
That specific verse is not quoted.
Various other verses are, for example: "There is salvation in no one else, for there is no other name under heaven given among men by which we must be saved" (quoted in paragraph 13) and "no one knows the Son except the Father and no one knows the Father except the Son and anyone to whom the Son wishes to reveal him" (quoted in paragraph 5).
And the document clearly states at the end of paragraph 11: "No one, therefore, can enter into communion with God except through Christ by the working of the Holy Spirit."