Quadrophenia was available on vinyl with stereo playback (and probably mono too, but I have only seen stereo copies).
If it was quadraphonic, why was it sold on vinyl appropriate for stereo playback? What would that offer?
Quadrophenia was not meant to be quadrophonic. Quadrophenia deals with a boy (Jimmy) who has split personalities (see any similarities to Green Day's "American Idiot" here?). Each personality was meant to be assumed by the 4 members of The Who. To quote the Wiki on the album:
To illustrate the four-way split personality of Jimmy, Townshend wrote four themes, reflecting the four members of the Who. These were "Bell Boy" (Moon), "Is It Me?" (Entwistle), "Helpless Dancer" (Daltrey) and "Love Reign O'er Me" (Townshend). Two lengthy instrumentals on the album, the title track and "The Rock" contain the four themes, separately and together.
Gotta love those old concept albums, and the way the material was tied together. :o)
While the album Quadrophenia was not recorded as quadrophonic, that was the first (and only) Who tour that was produced with quadrophonic sound. I saw it in Philly in 1973 (Dec. 4, I think). They had speaker columns set up in the back corners of The Spectrum. On the recording made for the King Biscuit Flower Hour, you can clearly hear Pete Townshend end his introduction of the album with the phrase "quadrophonic, of course . . ."
Incidentally, that same year I saw Pink Floyd for the first time. The Dark Side of the Moon tour was also done in quadrophonic sound. And virtually every Floyd concert since then - and every Roger Waters tour too - has kept the quadrophonic sound for live performances.