Catalyzes the demethylation of diphthine methyl ester to form diphthine, an intermediate in diphthamide biosynthesis, a post-translational modification of histidine which occurs in translation elongation factor 2 (eft201 and eft202). diphthine methyl ester-[translation elongation factor 2] + H2O = diphthine-[translation elongation factor 2] + H(+) + methanol Protein modification; peptidyl-diphthamide biosynthesis. Belongs to the DPH7 family.