"Google e Facebook declararam guerra aos sites de Internet que difundem notícias falsas, que o buscador e a rede social vão impedir que se beneficiem de seus serviços de publicidade."
"Google and Facebook have declared war on Internet sites that broadcast fake news that the search engine and social network will prevent them from benefiting from their advertising services."
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After the comma (which Google misses in its English translation), the word "que" (that) should be translated as "which" in this case. Also, the reflexive "beneficiar-se" (to benefit onself, used here in the imperative/command tense) seems to have confused Google, likely due to having missed the comma earlier. I took out the middle part of the second clause and translated only "que vão impedir que se beneficiem" and Google got it right, translating it as "which will prevent them from benefiting".
I have experience translating from BR-PT to EN (and even vice-versa for my own testing), and BR-PT native speakers have a habit of writing long-winded, run-on sentences in all sorts of published literature. I'm curious to see Google understand that aspect, which even trips me up once in a blue moon.