There were plenty of pieces of upper-body garments/clothing, which had a hood, before the 'hoodie'.
Was it simply that no one had thought of the name up until then? Or was there something different/special about the 'hoodie'?
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The OED says "A hooded sweatshirt, fleece, or other garment.", and therein lies the answer, I think.
A hoodie is a "hooded sweatshirt" or "hooded fleece", (in contradistinction to the original kind of each, which had no hood) and the abbreviation is natural.
As far as I know "hooded coat" or "hooded raincoat" have never become established phrases, and so have not become "hoodies". This may be because on an outer garment (especially a raincoat) a hood is unremarkable, whereas on a sweatshirt it is much more distinctive; but that bit is speculation.
Hoodie is simply a diminutive of hooded sweatshirt.
-y are very common diminutive suffixes in English, used for just about any word to convey "a slight degree of the root meaning, smallness of the object or quality named, encapsulation, intimacy, or endearment." (Wikipedia)
Other common examples include: