"Their dog drinks wine."
Translation:Ο σκύλος τους πίνει κρασί.
There is no need to use an article in this general statement in Greek, the same way it is not required in English. It is 'their dog drinks wine in general', not a specific amount of wine of a specific wine (e.g. the wine (that was on the table)). Some could even be implied, but including an article would completely change the meaning.
If anyone needs it, I found a way to write these Greek sentences with accents, since it doesn't provide any here. If you scroll over the English words it will give you their Greek underneath, and from there you scroll down to the word you want, copy it (Ctrl + c) and then paste it in the box (Ctrl + v). It works! Just make sure they're in the right order.