"He is demanding."
Translation:Tá sé ag éileamh.
It is being used as a verb here, yes. It also doesn't look like there's an samples of it being used intransitively. My guess is they meant it as an adjective and used it as a verb. Here's a list of possible adjectival forms
In the English sentence, “demanding” is a present participle, and in this sentence it could be interpreted either as part of a present progressive conjugation (e.g. “What is he doing? He is demanding.”, as an example of intransitive use) or as a predicative adjective (e.g. “What sort of man is he? He is demanding.”) As to what’s being demanded (the Irish sentence shows that the English participle should not be understood as an adjective), we don’t know, since it hasn’t been mentioned.
So would "Is duine éilitheach é" do for "He is demanding" as in "He is (a) demanding (person)?
It's not accepted because it's not correct.
You don't generally use the copula to describe someone/something:
tá sé déanach - "he is late"
tá sé fliuch - "it is wet"
You use the copula is to identify someone:
is é an múinteoir é - "he is the teacher*
or to classify/categorize someone/something:
is múinteoir é - "he is a teacher"
You can make tá sé ag éileamh more emphatic by using the copula, but you still need tá in there:
is ag éileamh atá sé
"He is demanding it" is a different construction: tá sé á éileamh