"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)?
No, this is the present progressive form. The translation for "he has demand" would be "tá éileamh aige" ...I think...my Irish is pretty bad. The passive would be "tá sé éilithe", according GnaG's notes on the Passive.