"All of his poetry is about love."
Translation:Onun bütün şiirleri aşk hakkında.
With other case languages, you have to learn "this verb takes this case" or "this preposition means X with this case and Y with that case." There are no exceptions where the case is not used. Turkish is very different in this way. Russian does not have a definite article either, but somehow it works out, I guess between saying "this car" and "my car," or "one car" or "some car or other." When it isn't clarified, it doesn't matter.
The 'onun' is included in the ending of şiirlerİ and - by the way - 'onun' is not the subject of this sentence. So why could I not leave out 'onun'? The only reason I could imagine would be that şiirlerİ can be translated as her/hıs or theır poems, means to avoid ambiguity.