Translation:My grandma reads the newspaper every day.
"My grandmother reads newspapers every day." should be accepted. Just more of the same problem with less exact or too exact English translation. You have to guess what the translator was thinking and not what would sound the best English translation. Because of this it is almost impossible to pass these tests, especially when Asian and other non-European languages are concerned. Somehow they are constantly trying to proove that my English is not good enough while I am having almost no problems with constructing Chinese sentences. So this is becoming funny and it is best to take it with a bit of homour....
In English an article is required here, unless you use the plural "newspapers".
The system needs the grammar to be correct in both languages, or it doesn't function properly. Besides, you can bet that native English speakers would otherwise complain, not to mention that it would give non-native speakers the wrong impression.
It's how we say it. We refer to it as a single entity, calling it "the newspaper" even though there may be several to choose from. However, you could also say "my grandma reads a newspaper every day", meaning one of the newspapers that are published daily (or you could use the plural "newspapers" without an article).