Where did the term "movie house" come from?
Solution 1:
The Oxford English Dictionary (OED) says the term movie(s) was first used in 1909. (Springfield, Mass and Philadelphia are two cities where this term was very first used, but the term became a national one lickety-split.)
The OED says that movie house was first used in October 1912 in the Altoona (Pennsylvania) Mirror. It was used in an Oshkosh, Wisconsin newspaper three months later (OED).
But even earlier is moving picture house, which appears in Moving Picture World volume 3 (1908).
Per the OED the term picture house was also in use as early as 1908 (Variety, Volume 23).
Given that movie is short for moving picture, one can say that movie house is short for moving picture house (which appears to be the earlier term).
I wouldn't be surprised if the term motion picture house was not also in use; indeed Google Books has 1915/1916 uses. The term motion picture appears to predate moving picture.
As far as the term house goes, earliest (late 19th century) motion picture projections (as opposed to machines that individuals looked into) often took place in the auditoriums of variety houses, playhouses, and even opera houses; so the terms movie house, (moving) picture house, and motion picture house seem to have arisen naturally, by extension.
The Edison Phonograph Monthly, in which I found a February 1912 use of moving picture house, was published in New York from 1903 to 1916. Compare the names of other early periodicals devoted to the new industry, including but not limited to
Moving Picture World, from 1907
Motography: Motion Pictures, from 1909
Motion Picture, from 1914
The Picturegoer, from 1915
Motion Picture Classic, from 1920
Picture Play, from 1922
etc, etc, etc, etc, etc
Given that the sweeping, ground-breaking film Birth of a Nation came out in 19151, that the term movie house was already in use at least as early as 1912 shows that it and related terms were contemporaneous with the quickly advancing motion picture industry.
1 See for example 23 Feb 2016's "Unjust and unworthy portrayal:" "The Birth of a Nation" in the Smithsonian's blog O Say Can You See?
NB that the 19th century returns in a Google Books search for 'movie house' are all spurious. Upon examination and further research it can be seen they are all scanning errors or from sources first published in the 20th century. This is also backed by the OED's citation of movie not appearing before 1909.
Solution 2:
Although (according to AmE speaker's informative answer) the OED identifies as its first occurrence of "movie house" an October 12, 1912, instance in the Altoona [Pennsylvania] Mirror, a slightly earlier occurrence appears in an Arizona newspaper (reprinted from the Los Angeles Times). From "Infantile Paralysis in Coast Resorts," in the [Phoenix] Arizona Republican (August 6, 1912):
At a Spring street 'movie house' [in Los Angeles] last night thirty persons were turned away during the course of a few minutes and the fair ticket seller said that the same condition prevailed all day.
Another 1912 instance arises in "Popular Shows Good Pictures," in the Honolulu [Hawaii] Star-Bulletin (December 9, 1912):
The prices of admission are only fifteen and twenty cents, and the changes of pictures will be as often or oftener than any other "movie" house in the city. Take in the Popular.
Multiple instances appear in other parts of the country, notably New York City (January 10, 1913); Irvington, New York (January 10, 1913); Tombstone, Arizona (April 6, 1913); Missoula, Montana (June 3, 1913); Leadville, Colorado (June 25, 1913); Rock Island, Illinois (July 1, 1913; Hammond, Indiana (July 21, 1913); Telluride, Colorado (August 7, 1913); Roanoke, Virginia (August 14, 1913—reporting a story from Seattle, Washington); Santa Cruz, California (August 14, 1913—same); Pendleton, Oregon (August 15, 1913—same); Fort Collins, Colorado (August 15, 1913—same); Sacramento, California (August 19, 1913); El Paso, Texas (August 24, 1913); Salt Lake City, Utah (August 31, 1913; and Washington, D.C. (September 1, 1913)—all within 13 months of the first occurrence that an Elephind search finds.
The two most noticeable things about this list of towns and cities are (1) how many unique localities there are (three from 1912 and fifteen more through September 1, 1913; I omitted links to second and later occurrences from any of these municipalities), and (2) how many of them are in the western third of the United States (twelve of the eighteen). The likeliest place of origin of the term "movie house" as a short form of "moving picture house" is Los Angeles, California; but regardless of where it originated, the term seems to have spread nationwide in the United States very quickly.
Previously, I neglected to run a search for early occurrences of the plural form "movie houses," but an Elephind search returns a number of them as well, including one that antedates the earliest Elephind match for the singular form. From a headline in The Player (June 28, 1912):
Denver's Big Movie Houses
The Player, a New York–based theatrical, film, and performance periodical with a national audience, uses the term "movie houses" in two other 1912 headlines, as well—on October 4 ("Martha Russell in 'Movie' Houses") and on December 27 ("Canadian 'Movie' Houses Win Their Fight for Sunday Shows").
Other 1912 instances of "movie houses" appear in Hammond, Indiana (August 28, 1912) and Los Angeles, California (November 22, 1912); and occurrences from the first eight months of 1913 include matches from Chicago, Illinois (February 25, 1913), Tacoma, Washington (March 5, 1913), Clare, Michigan (March 21, 1913), Omaha, Nebraska (June 24, 1913), Seattle, Washington (July 24, 1913), Milford, Michigan (July 26, 1913), and South Bend, Indiana (August 16, 1913).
The new first-time results increase the representation of cities from the U.S. West and (especially) Midwest. Again, the overarching sense I get is that the term "movie house[s]" swept across much of the country in little more than a year after the earliest reported Elephind match, from the June 28, 1812, headline in The Player.