Or as one dictionary puts it, "one who insists upon the minutest grammatical niceties." Like all of the derogatory -aster words, there's a strong connotation that the grammaticaster is often incorrect -- so the sort of person who insists that "He is tired" is in the passive voice because it has a form of "to be" is very much a grammaticaster. Coined on the model of poetaster (inferior poet) from Greek grammatikē, grammar + Latin suffix -aster, a diminutive or pejorative suffix denoting something that imperfectly resembles or mimics the true thing (not necessarily a person -- tofukery can be called carnaster). Note that the stressed penultimate syllable is a short A.
I'm not looking forward to spending Thanksgiving with a literary pedant and a grammaticaster.