Catalyzes the demethylation of diphthine methyl ester to form diphthine, an intermediate diphthamide biosynthesis, a post- translational modification of histidine which occurs in translation elongation factor 2 (EEF2) which can be ADP-ribosylated by diphtheria toxin and by Pseudomonas exotoxin A (Eta). {ECO:0000250|UniProtKB:P38332, ECO:0000269|PubMed:19965467, ECO:0000269|PubMed:23486472}. This is the function of DPH7 (diphthamide biosynthesis 7, Ensembl gene identifier ENSG00000148399).