The American Heritage Dictionary does not disagree:
storey. The American HeritageŽ Dictionary of the English Language: Fourth Edition. 2000.Chiefly British Variant of story
BTW, Merriam-Webster just has it down as a variant, rather than a BrE spelling:
Definition of story - Merriam-Webster Online Dictionary
Why is it a proper word? Because that is the British spelling:
Cambridge Dictionaries Online - Cambridge University Press
You seem to be implying that American English is the only variant that is acceptable. We don't agree; users use their own spellings and their own variants. We have British, Canadian, American, Pakistani, Indian and other contributors. I, for instance, am a British English speaker, so I use BrE forms and spellings. English is an international language and the usage on this site reflects this.
Our view is laid out here: https://www.usingenglish.com/profile...es/000353.html
and here https://www.usingenglish.com/about.shtml
Our view of another bugbear for some American speakers is here: https://www.usingenglish.com/profile...es/000358.html
Much of the site is written in British English, simply because most of the contributions have come from BrE speakers.