C.V. Sauveur, whose first name was "Clarence," died in September 1976. The current proprietors' statement that they established their business in 1977 may indicate that they bought it from Mr. Sauveur's estate shortly after his death. According to real estate records, the current building was constructed in 1959, when it still would have been owned by Mr. Sauveur.
Aerial photos of the area, taken from Historic Aerials, show that the plot had a number of buildings as of 1951. These were presumably the "cabins" described on your matchbook cover. The current L-shaped building, which appears in the 1962 aerial photo, occupies the footprint of some of the earlier cabins.
I believe that the pond that appears behind the Inn buildings in the 1951 photo, marked with a yellow arrow, is the quarry from which the business took its name. In the current Google Maps screenshot, you can see that it has been filled in and paved over. The quarry was originally operated by Joseph Tinner, for whom nearby Tinner Hill is named. Tinner was an early civil rights activist who is credited with establishing the first rural branch of the NAACP. He passed away in 1928. A stone arch across Lee Highway from the Quarry Inn commemorates his life and these events. Stones for the arch were salvaged from buildings in the area that had been constructed with materials from the quarry.
Sisler Stone, which still operates immediately next door to the Quarry Inn to the east, is a successor business to this quarry. The Sisler family first opened a monument business in Winchester, later moving to the Cherrydale section of Arlington before bringing their business to the current Falls Church location in 1937. It is interesting that this is the same year as the handwritten notation on your matchbook, although that could just be coincidence. Some Falls Church historical literature refers to this location as the "Sisler quarry" and inaccurately attributes the stone in buildings constructed well before 1937 to Sisler. It is possible that the Sislers may have quarried the area for a short time after they established their Falls Church business, but if so they must not have continued for long. According to historical descriptions for Sisler Stone, their primary source for materials, even before World War II, was a quarry near Haymarket, Virginia.