Here is the actual Winter Garden marquee just 3 years before WEST SIDE STORY opened. From numerous photos from past shows -- ranging from this 1954 PETER PAN marquee, to FUNNY GIRL in 1964, MAME in 1966, FOLLIES in 1971, 42ND STREET in 1980, CATS in 1982 thru 2000, to even its current resident MAMMA MIA! -- the name WINTER GARDEN name has never been replaced by the show's title. Also, the Winter Garden marquee is quite long in length and does not have that pot/cup/whatever above it -- its always had that enormously wide billboard.
Of ALL people, the Library of Congress should know the difference. Apparently all those other sites are under the same assumption about the Library of Congress and captioned this photo as: Opening Night, Winter Garden, New York... when it ain't so.