No permission is required because the design is in the public domain and the uploader's recreation is a faithful reproduction of the public-domain design. The dust jacket was first published prior to 1978, and it is believed that it omitted a valid copyright notice. Rivers and Mountains was first published in 1960; the hardcover book itself carried a copyright notice, so its contents remain copyrighted. However, dust jackets were required to carry a separate copyright notice for independent protection of their design. According to The Compendium of U.S. Copyright Office Practices: Chapter 2200, § 2207.1(C) at p. 15:

"A notice of copyright on the dust jacket of a book is not an acceptable notice for the book, because the dust jacket is not permanently attached to the book. Likewise, a notice appearing in a book is not an acceptable notice for the dust jacket or any material appearing on that dust jacket, even if the book refers to the jacket or material appearing on the jacket."

This edition of the book is quite rare, and unfortunately there is no complete scan of the dust jacket available online. Certainly the cover and the back cover omit a copyright notice, but the dust jacket flaps are not available online. However, there are numerous complete scans/photosets showing other dust jackets published by Holt, Rinehart & Winston in the 1960s and early 1970s, and none of them include a valid copyright notice. See, e.g., the dust jacket of Cat's Cradle (1963) by Kurt Vonnegut at Commons, or the dust jacket of The Bluest Eye (1970) by Toni Morrison, both published by Holt, Rinehart & Winston. Rivers and Mountains was published in 1966, between the publication of those other two books, and it is almost certain that this dust jacket would have also omitted a copyright notice.

Keep in mind that the pre-1989 requirements for copyright notice were highly formalistic and, other than a few enumerated exceptions, required these three elements:

1. "The symbol © or the word 'Copyright' or the abbreviation 'Copr.' or an acceptable variant such as "(c)";
2. "The year of first publication for the work"; and
3. "The name of the copyright owner, or an abbreviation by which the name can be recognized, or a generally known alternative designation of the owner."