One could argue that Spanish is an adjective and is also a noun, as are English, German, Polish, etc. The man who did the translations from Elvish languages to English in the LotR movies uses the word "Elvish" as a noun. Tolkien himself used the terms "Dwarvish", "Mannish" and "English". I see your point in which the proper use of "Elvish" would be as an adjective, but I feel that it can be used as a noun to refer to Elvish languages broadly. I understand and respect your opinion though. :)
Tell me: How many languages can you refer when you say “Spanish”?
A - One
How many languages can you refer when you say “German”?
A - One
How many languages can you refer when you say “Dwarvish”?
A - One
How many languages can you refer when you say “Elvish”?
A - NOT one!
Why Tolkien sometimes used the term?
A - Because he was kind with lay people. We even used the Gregorian calendar!!! You know…there is no September in Middle-Earth!