We're off is always present tense. In your sentence, it's used to refer to a present-time event.
Yes, point taken. I meant that in this case, it was used for a present time event, as opposed to all of the previous examples, including your translation of "He is off to ..." as possibly "He will shortly be on his way", which is future 'tense'.
"We're off to see the wizard" has context, so we know it can't be rendered as "We will be on our way to see the wizard".