That’s bizarre, is the owner British or something? “Here or to go?” is the standard in the US as far as I’m concerned.
First, _go_ is older than _away_. According to Etymology Online, go dates back to Old English ("gan"), while away in sense of "at a distance" is from 1712. Second, I get to save a syllable.
So "to go" is older and less effortful than "takeaway". Also, both work.