Because 'die' can also be a demonstrative pronoun. But I think it's not a good idea to present these translations to learners. It's confusing. From the written sentence you can't distinguish the article 'die' from the demonstrative pronoun and taking it to be an article is by far the more natural interpretation.

Well Zeitung is feminine, and this is the accusative case so the proper article would be die.

no, it's wrong.