Is vomiting a mandatory symptom for diagnosis of binge eating disorders?

No. Self induced vomiting is the most common method to compensate for binge eating episodes in the purging type of bulimia nervosa. Others include misuse of laxatives. Diuretics, enemas. However there are other methods of compensating which include excessive exercise and fasting classified as the nonpurging type.
Binge eating. No. This diagnosis does not include purging or fasting or excess exercising.