You are literally correct!, but when translating from Portuguese to English "this" is used more often than "it". Therefore it should be an accepted answer. Many times you say you cannot translate word for word but that is exactly what Duo is doing in this case. DUO does not accept what is normal in English. It is like "Voltar", Duo says "come back", which many people use, but I say "return" which is the actual translation for "Voltar " to return. English is my first language, but I learned Spanish in high school in the late 50s, and "come back" would never have been accepted as an answer for Voltar.
I'm sure you personally are way beyond the need for any answer but other people who are new read these discussions so I will answer anyway. :)
"Whose shirt is this" introduces another word into the sentence which has a Portuguese equivalent (esta).
Repeating Paulenrique's comment above:
A tip for Duo: when "é" comes by itself refering, translate it as "it is". Your sentence would probably be accepted if the original sentence were "De quem é ESTA camisa?"
So, perhaps, "Whose shirt is it?" would be best for English speakers to accept.
"Who's" means who is (or who has) so unless, "shirt" is a proper name or perhaps job position, that won't work.
"Whose" is the possessive of who.
But I agree, "Whose shirt is it?" flows better; though the other [DL translation] works just as well and would get the business of understanding done.