Grammarist is not a dictionary-approved word. It specifically relates to this website.
The term for a person who specializes in grammar is a grammarian. Also, someone who creates or standardizes a syntactical construct is a grammarian.
The word grammar has largely stayed unchanged from its Latin root of gramatica.
As you can see by this n-gram, the usage of grammarian has dwindled over time.
Side note: in the French version, grammairien, the word used to also carry the meaning of magician.
Examples
Grammar is the sentence structure and language rules for our English language, and it is not taught through texting or writing on the computer, tablet, or iPad. [Sierra Vista Herald]
The grammar debate in marketing is not new. The Winston cigarette brand was famously taken to task for “Winston tastes good, like a cigarette should.” Grammarians gave them millions in free publicity by arguing that “Winston tastes good as a cigarette should.” [Forbes]
Until recently I thought Panini was a Mediterranean sandwich and then to my shame found that it was the name of the grammarian who codified the syntax of Sanskrit. [The Asian Age]
The Grammarist supports understanding of English grammar rules through a clear, concise and easy to use platform. Some of the numerous options include common mistakes in terminology such as affective vs. effective, use and explanations of common idioms, colloquialisms (a word or phrase that is not formal, but rather local lingo), parts of speech, easiliy confused words, word phrases, homophones and much, much more. [College of Medicine, Saudi Arabia]