Wikipedia is an encyclopedia with a firm no-first-hand-research policy; i.e., any fact contained in any article must be supported by a reliable source. Wikipedia itself (nor its contributors) has nothing to do with it.
So there can only be two reasons for those numbers in the Wikipedia being different from Guiness' numbers:
Mr. Scheidel explains (a little bit) about his reasoning for his numbers; a footnote mentions that he uses "conservative corrections for the persistent underestimating of ancient population sizes" compared to his own, older source.
He goes on to state "it must be stressed that most of the numbers are merely rough approximations, best interpreted as the center values of wider ranges" , and "offer at least a sense of relative magnitude and broad patterns".
In that regard, I would suggest to view all this with an open mind - nobody has actual numbers for populations BCE, and it is clear that even where there are rare written traditions, numbers of general populations or armies, and so on, are often significantly inflated or deflated (i.e., the survivor of a conflict might inflate the enemy numbers, and deflate their own, to appear more heroic). Even assuming that the true numbers were actually known back then, with no general census or other reliable method to count them...
Guiness doesn't give a source, at least not in the article you linked, and I don't know their source policy.
If I were forced to decide between the one or other, I'd go with Scheidel's, purely because he seems to be relatively transparent about his source and procedure.
But the most important aspect is to be mindful that even the research paper is just that - scientific research. It is only a theory, and its truth value only consists in how long it takes to refute it. In this special case - ancient history - it is very close to being irrefutable (because we simply don't have any new methods to count the populations now, unless we invent a time machine), and thus is - same as 99% of other accounts of ancient history - just a tiny step above pseudo-science if taken as "absolute". (Don't get me wrong, articles like this are probably perfectly fine science if taken in the spirit of talking about the "history of history" - i.e. about the activity of doing historic research itself is the subject matter.)