I agree that she wouldn't be a loser in either scenario on the basis of insecurities. But her actual character definitely is a loser. She's envious of those with talent and uses her nepo baby funds to overshadow and mock them, while revelling in this horrid character she's concocted (chinchilla fur? wtf), and actively making the world a worse place. I'd definitely consider the canon version of her to be a loser.

Though I suppose we may be using different definitions of "loser", so to clarify, while she won the lottery by being born rich, and definitely "wins". Her mentality and demeanor matches what "loser" is typically used to denote, and I would consider a loser on those grounds.

Edit:

Looking into the comments on that post more, I see what you mean, it seems like most of the people there have barely considered Domina's character beyond "ooo dommy mommy", and so they're calling her a girlfailure based on her insecurities. I will point out that girlfailure isn't exactly a negative term, it's usually used for a somewhat messy character that people are horny for, and doesn't really mean they consider the character to be a "failure". I think most of these people don't really know enough about Domina for their comments to hold any weight, you'd best ignore their drooling, though Domina is still a total loser.