That is another possible translation.
German doesn't distinguish grammatically between something that is happening right now (where English would use present continuous: we are drinking) from something that happens regularly (where English would use the present simple: we drink).
So without a context which forces one of those interpretations, both English translations are possible.
Isn't Trinken = Drink?
No. "=" is not particularly helpful when learning languages since German is not a code for English, so it's often the case that there can be more than one translation for a given word.
I have seen Trinken been used with Wir before.
Sure. wir trinken = "we drink" or "we are drinking".