There are two parts to this question:
Does the Book of Job refer to a spherical Earth?
If so, did it beat the other contenders to be the first to have the idea?
I don't propose to properly answer Part 1. This is a question for Hermeneutics.SE, not Skeptics.SE.
I will note the obvious: the modern English translation provided is clearly not evidence to support it, as it is too vague and wouldn't suggest a spherical Earth to someone who wasn't looking for such a reference.
Also, I have not seen any reports of Rabbinical scholars taking the idea of a spherical Earth seriously prior to much later, which suggests maybe the original version didn't suggest a spherical Earth to them either. I am open to hearing of reports I missed.
The cited text admits that the Greeks suggested a spherical Earth in the sixth century BC.
Historians generally [wrongly] credit the Greeks with being the first to suggest a spherical earth. In the sixth century B.C., Pythagoras suggested a spherical
Wikipedia explores the history in more detail. While it was credited to Pythagoras (6th century BC), it can't reliably be ascribed to him.
Plato (427–347 BC), on the other hand, explicitly stating the Earth was round, and Aristotle (384–322 BC) has providing justifications and Eratosthenes (276–194 BC) estimated its size to within 15%.
The dating of the book of Job is even less clear.
The Book of Job is dated at 6th-4th Century BC by Katherine Dell, p337, with no clear citation.
A Straight Dope column delves into the controversy, suggesting the stories evolved and changed.
It argues that the stories are believed to be much older (e.g. 1700 BC) and may have been first recorded later (around 1000 to 800 BC) and then the "poetic middle section" added later still, "perhaps written around 6th Century BC." or even later.
The poetic section has some parallels of thought with the second Isaiah writer (around 540 BC), but which came first, there's no way of knowing. Job is mentioned by Jeremiah, so probably the book as we know it was finished by (say) 600 BC, although some date it much later--for example, Jeremiah could have known the folktale, but not the poetry.
He goes on to point out that it may have just been one author at the later date. Whether it was just one author or many, we have to take the last one for the reference.
I am ignoring nonsense estimates like Ussher and Anderson, which are based on the claimed ages of the characters in the stories.
So where does that leave us?
If the poetic sections are referring to a spherical earth, and the scholars are right about the age of the Book of Job, then we find that it was probably written after Pythagoras, and perhaps even after Plato, but possibly before either of them.
So, neither had clear priority.
Again, if the answer to Part 1 is "No, this is post-hoc rationalization, reading more into a poem than the original author could have intended", these datings are irrelevant.