Let me expand my comment into an answer.
The most natural interpretation that occurs to me is that eo is the ablative of id.
This ablative is causal, meaning "for that reason".
I believe you could substitute ea causa if you wanted.
I would translate the passage as "…mocked him for the reason that Polybus…".
Here "for the reason" is eo and "...
H. J. Rose points to two characteristics of Hyginus's Latin that are considered substandard:
"Overworked" relative pronouns
Poor translations from Greek
Rose gives one example of the "monotonous use" of relative pronouns, from chapter 55 of Fabulae, though he remarks that such use can be found in "almost any passage" of Hyginus:
qui cum conatus esset a ...
"Contest" from L&S's definition 2 works pretty well here: "he appointed this contest for Jason". "Issued this challenge" might be better yet. I think this is a slightly unusual use of simultas in that this "contest" is not between Jason and anyone else, so the word doesn't seem to convey a specific connotation of hostility as it otherwise would.
Well, as I read more of Hyginus, I'm beginning to get a sense of at least some places where the Latin feels inelegant. For example, in "Parerga [Herculis]," he writes
[Achelous] cum Hercule propter Dejaniræ conjugium cum pugnaret, in taurum se convertit, cui Hercules cornu detraxit, quod cornu Hesperidibus sive Nymphis donavit, quod deæ pomis replerunt et ...