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(Ms.) Pacman? ;)

Or are you looking for something like Teddy in D4 - Dark Dreams Don't Die? ;P

Anyway, if we're talking about games only, I don't think any of the issues you list are really common. Drink and drugs may be used for flavour and giggles, but to my knowledge alcoholism and drug addiction aren't often themes in videogames either. And depression (which I wouldn't classify as 'glamorous' at all) only more recently, mostly in narrative indie games, adventures, visual novels. That's where I would look for the theme of eating disorders, too, at least if you want it to be treated seriously. Can't imagine many action games including something like that as anything other than a cliché. There's a high risk that it would feel out of place, preachy and/or superficial, in any case.

Here's one in a Choose-You-Own-Adventure style, Mangia by Nina Freeman.

Let's see: If I use Google to search itch.io for anorexia, we do get a couple hits:

https://bedtimephobias.itch.io/shrinking-pains (free)
https://crowgirl.itch.io/hackers-versus-banksters ($5)

(Of course, any game that could be recommended in this thread should come with a content/trigger warning, as eating disorders can be triggering for many people, particularly those who've suffered through one.)

Well there is this hilarious scene from San Andreas : https://www.youtube.com/watch?v=A6g0mPo-uJM

In the new release, "Attack of the Earthlings", they eat people. PEOPLE! If that's not an eating disorder, I don't know what is!

https://www.gog.com/game/attack_of_the_earthlings

Looks fun. I need to check out some Let's Plays and reviews.

Interesting that you only searched for anorexia and not also for adiposity/obesity.

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The character I first thought of was from a Wii game, but I think it's ambiguous as to whether or not she has an eating disorder. Some people apparently argue that the PC's response to NPC might actually cause an eating disorder in the character that she didn't have to start with.

Eunice from Rune Factory Frontier.

I found the comments here on the same character are interesting.

There's Gadan in Grandia 2. He's possessed by Valmar's tongue. That dude doesn't have an eating disorder, he IS an eating disorder. He (The Tongue of Valmar) even eats one of your party members oO

Does King Hippo count?

Downfall (both original and redux version) treats obesity and bulimia among other disorders.

https://www.gog.com/game/downfall_redux

This guy. Probably the 2nd most difficult fight in the game too.

Eddie from Silent Hill 2 is hinted at having an eating disorder due to his trauma. But it's incredibly subtle to the point of being non-existent. He is seen eating in one scene and puking it up in another, which hints that he's become bulimic.

And I think this counts:
https://www.youtube.com/watch?v=Au7UYaqpJw8&feature=youtu.be&t=39

Not an eating disorder, but one of the playable characters in Shadow Hearts: FTNW is a vampire that has to manage her calories and depending on her calory level she takes on a different form (Bat, chubby or slim).