Why is jiH needed in this sentence? Or if not needed, I'm not sure how it fits in grammatically since ji- already defines the subject as me (I).
It's not needed. It's optional.
jIyajbe' and jIyajbe' jIH mean the same thing ("I don't understand").
The second one might be a little more explicitly that "I don't understand".
Similarly, qayaj "I understand you" could also be said as SoH qayaj or SoH qayaj jIH or qayaj jIH with one or both of the implicit pronouns stated explicitly.
This course usually omits pronouns but occasionally includes them so that you will see that kind of sentence as well.
And in the third person, pronouns can be useful to distinguish between 'oH and ghaH (it, incapable of speech versus he/she, capable of speech) and for bIH versus chaH (they, incapable of speech versus they, capable of speech). But even there they are not grammatically required -- chaH yaj ghaH and yaj can both mean "He understands them", though the first one is clearer.