Sweat equity doesn't occur in a vacuum; something is created from that effort. If they wrote code and that code earns money, they are entitled to a portion of those earnings. That's inarguable.
It is my understanding that the original "idea" (I have trouble calling it a company) didn't take hold. If nothing is created and the company never amounts to anything...what are you getting an "ownership stake" in?
Had Zuckerberg and a friend opened a candy store on the Harvard campus in 2002, and it had failed, that friend is not entitled to anything Zuck does with Facebook because he put in labour on the candy store. Now, if Zuck was operating Facebook under the same legal entity as the candy store in which his partner had equity, said partner might have a claim, though it would be hard to establish if the partner produced no work for the new idea. That said, if this is analogous to the situation in the article, what on earth are these guys doing getting bogged down with convoluted equity agreements when they should be working on the product?
I'll repeat: if the other co-founders provided something tangible --be it an idea, code, money, whatever-- to the new project, they deserve "their share". If they can't point to something tangible, they deserve nothing.