I have been looking for a word to describe a group of people that are very loyal and passionate about their (native) language.
chauvinism could be used aptly in such a circumstance along with a suitable descriptor. Note that it is usually used in a negative light.
Chauvinism refers to extreme prejudiced support for some cause.
So, linguistic chauvinism for language would be similar to patriotism for country.
I couldn't find a single word, but a good example of what you are describing are the Gaelic language revivalists in Ireland. The term that appears most often is "language enthusiast". See below
I don't know if this works for all languages, and it doesn't quite fit your phrase with the blank, but Yiddishist works specifically for Yiddish.
Yiddishism: a movement characterized by advocacy of the Yiddish language and culture
(The advocacy is needed because Yiddish is dying out.)
That would be a logophile http://www.dictionary.com/browse/logophile
noun 1. a lover of words
Or, to fill in your title question, 'Patriotism' is to 'Country' as 'Logophilia' is to 'Language'.