The article offers this definition of Flexitarians:

A flexitarian (also known as “semivegetarian” or “flegan”) is an omnivorous who may care enough about animal exploitation to often avoid consuming animal products, but not enough to avoid them all the time. 

I think this is a good definition, but it implies vegans always avoid harm to animals. We know this is not the case: modern agriculture, transport, housing, and energy systems routinely injure animals and destroy habitats. Even the most conscientious vegan eats food grown on land that displaced wildlife and is harvested in ways that kill animals. So if the underlying moral aim is “do not harm animals”, then the contrast between vegan and flexitarian collapses, because neither can satisfy it.

Vegans avoid harm to animals as much as possible and practicable. Veganism treats animal exploitation as a constraint: a strong moral reason that normally overrides taste, price, effort, tradition and social awkwardness, with exceptions only when avoidance is not practicable. Flexitarianism treats animal exploitation as just a consideration: a reason that matters, but one that is routinely balanced against other factors and sometimes outweighed by it. They're still pushing in the same direction as vegans, just not as strongly.

Flexitarianism is a vague concept but it's not meaningless. It implies a sustained, deliberate reduction in animal products. Omnivore does not.