Here's as much of the history of the Rotograph Co. as I've been able to piece together. There must be more information out there, so I'd be happy to hear from anyone who can fill in the gaps.
The company appears to have been active as a publisher of postcards from 1904 until 1911. It was formed from the merger of the National Art Views Company (active 1902-1904), based in New York City, with the American branch of the Neue Photographische Gesellschaft, founded in 1894, which apparently was the corporate parent. The latter firm may have used the Rotograph name for a line of photographic paper for several years before this. Arthur Schwartz, the company's president, directed overall operations from Berlin; the vice-president, Ludwig Knackstedt, supervised its factory in Hamburg; and the former proprietor of the National Art Views Company, Frederick Schang, became the general manager of Rotograph's American operations. The firm also reportedly had factories in London, Paris, and Milan.
According to a contemporary account in The American Stationer, in 1905 or very early 1906 Rotograph consolidated several offices and warehouses at 771 East 164th Street, 395 Broadway, and 3621 Third Avenue into a new facility in the Mercantile Building at 684 Broadway.
The Rotograph Co. reportedly published around 60,000 images using a variety of printing techniques and styles, and encompassing a wide range of themes in addition to scenic view cards. In some cases, they appear to have produced proprietary cards for local druggists or stationers that didn't display the Rotograph name, although the connection to the company (or to its European affiliates) is evident. Below, for example, is a postcard published by "E. Farrington" of Tarrytown, NY. The typography and layout are identical to Rotograph's H series, and the number (9109) seems to follow the company's numbering system for that line. (The card shows two buildings, since extensively restored, that are now part of Philipsburg Manor in Sleepy Hollow, NY.)
By March 1911, in spite of or perhaps because of its enormous output, the Rotograph Co. no longer existed as such, and the sale of its assets was reported in the Bookseller, Newsdealer and Stationer:
The Rotograph Co., well and favorably known to every dealer as makers of "Post Cards of Quality," have recently been absorbed by the Illustrated Postal Card & Novelty Co., 520-524 West Forty-eighth street, New York, whose plant is now said to be the largest one in the United States devoted exclusively to the manufacture of postcards. They employ 500 people. Their factory is equipped with special postcard machinery of every description, and operated by German experts in the line. Their product is therefore of the highest order, and can be delivered in quick time, and at a low price. Among the assets obtained from the Rotograph Co. is the largest collection of real photographs in the world, comprising thousands of art subjects, old masters, life models and over two million photographic views [emphasis added] from every nook and corner of the United States. The Illustrated Postal Card & Novelty Co. have just finished classifying this immense collection, and are putting the photo views at the free disposal of their customers who place view card orders. This latter inducement, no doubt, ought to bring them large view orders. — Geyer's Stationer.The Metropolitan Postcard Club website lists two "Illustrated Post Card" companies, one (probably unrelated) in Quebec and the other, active 1905-1914, at 520 West 84th Street, New York, NY, the same address as the one given above. In fact the Illustrated Post Card & Novelty Co. seems to have lasted until at least 1918, but it doesn't appear to have amounted to much as a successor to Rotograph, and in any case importing high-quality cards from Germany was ended with the outbreak of the Great War. I don't know what became of the "two million photographic views" or other company archives. As for the German parent company, which presumably had liquidated its interest at the time of the sale, the Neue Photographische Gesellschaft remained in business until 1948.
Sources: General information: the websites of the Metropolitan Postcard Club and Rotopex (the latter site is no longer available). Information on Rotograph's relocation and its executives and printing plants is from The American Stationer, January 6, 1906, p. 4. The report of the acquisition of the company's assets by the Illustrated Post Card & Novelty Co. is from the Bookseller, Newsdealer and Stationer, March 15, 1911, page 188, where it is in turn attributed to Geyer's Stationer. Advertisements for the Neue Photographische Gesellschaft's bromide "Rotograph" paper can be found in many trade periodicals from the first decade of the 20th century, including the St. Louis and Canadian Photographer in 1900, where the NPG's address is given as 7 West 14th Street, New York City.
Hearings in the US Congress on the Revenue Act of 1918 include testimony that the Illustrated Post Card Novelty Co. (without the ampersand) had manufactured and sold 75,000,000 cards in the previous year, but projected sales of only 15,000,000 in 1918 due to an increase in postage from one to two cents. The Postcard Album website declares that Arthur Schwartz "established the Rotograph Company in New York for the automatic printing of photographs in 1892," thus predating the founding of the NPG itself. The precise relationship between the various corporations involved remains unclear to me, but in any case it seems that the Rotograph name was not used on postcards until 1904.