Amidase that catalyzes the last step of diphthamide biosynthesis using ammonium and ATP. Diphthamide biosynthesis consists in the conversion of an L-histidine residue in the translation elongation factor eEF-2 (EEF2) to diphthamide (By similarity). ATP + diphthine-[translation elongation factor 2] + NH4(+) = AMP + diphosphate + diphthamide-[translation elongation factor 2] + H(+) Protein modification; peptidyl-diphthamide biosynthesis. Belongs to the Diphthine--ammonia ligase family.