I wonder why this is "die Zeiting". The newspaper is being acted upon, so in the same way that "... eats the apple" becomes "... isst den Apfel" (and not der Apfel), why isn't this sentence "Sie liest der Zeitung"?
Answering my own question...
It's because only masculine nouns are affected when being acted upon (i.e. accusative). Feminine and neuter nouns continue to use "die" and "das" respectively. The table here is helpful: