Binge-eating is usually done in secret, and that shows up quite a bit on Sesame Street, as the majority of Cookie Monster's freak-out scenes are done solo. Notice in the above video that he doesn't dive straight in until the other character leaves the room. That doesn't happen every time, but it happens enough to be considered a symptom.
It's not his fault. He's not just a greedy, gluttonous asshole who hogs all the food. There are many reasons why Cookie Monster might binge-eat: a chemical imbalance in the brain, genetics, severe emotional or physical trauma. I could definitely see that last one happening after he ate Ernie's X and later had to pass Styrofoam through his poor monster butthole.
Unfortunately, Cookie Monster's condition is worsened by the way the other characters react to his behavior. They either try to take the cookies away from him, even though food restrictions actually promote binge-eating (found at 22:00 in the following video), or they give him cookies as a reward for completing a task successfully (12:00 in the same video):
It's essential that Cookie Monster learns the underlying emotional reasons why he turns to food for help, along with coping strategies to use when he becomes emotionally distressed. Cognitive behavioral therapy, dialectical behavior therapy, internal family systems, and trauma therapy have all shown promise in doing this. What does not help at all is people clearly enabling his behavior while he lets his disorder completely dictate and obliterate his emotions. Seriously, watch this video, and you will see Cookie Monster in a completely different light: