I'm thinking that it is a punctuation problem, and that the sentence can be fixed with a couple of dashes: "The debate over Bain Capital and its ventures--how many jobs were lost vs . how many jobs were saved at companies they acquired and who profited--is absurd and makes no earthly sense."

Yes your understanding of the structure is correct. The sentence is not grammatically correct, only because it lacks important punctuation. You can either use en-dashes, em-dashes, or brackets. All three options are fine. Personally en-dashes would be my first choice, brackets next, and em-dashes are not my style at all. "The debate over Bain Capital and its ventures - how many jobs were lost vs how many jobs were saved at companies they acquired and who profited - is absurd and makes no earthly sense." "The debate over Bain Capital and its ventures (how many jobs were lost vs how many jobs were saved at companies they acquired and who profited) is absurd and makes no earthly sense." "The debate over Bain Capital and its ventures--how many jobs were lost vs how many jobs were saved at companies they acquired and who profited--is absurd and makes no earthly sense." Note also, I have removed the period after the "vs". It can be kept or omitted, but if you want to keep it, you should remove the space between the vs and the period that follows it.

You are correct it is needlessly complex. I would modify it this way: The absurd debate over Bain Capital and its ventures centers on how many jobs were lost vs saved at the companies they acquired while certain people profited. Trying to add the description at the end makes it an awkward phrase. Repetition of 'how many jobs' isn't wrong, but only needs to be used once.

The sentence is correct and means: "The debate over Bain Capital, how many jobs were lost versus saved at acquired companies, and who profited is absurd and makes no sense."