This term is a reduction of the phrase
malt alternative, and it implies that these drinks are meant to be an alternative to that slightly more famous category of malt-based beverages: beer.
Malternatives have been a near-fad since the early 2001 release of Smirnoff Ice, but the word itself is a few years older.
A different sense of this term a microbrewery (a term that dates from 1982) is quite a bit older. In an October 4, 1989 People magazine article titled "Radicchio ad absurdum! Or, 80 Reasons Eating Was the Great Adventure of the '80s," here was reason number 33: "Micro Breweries: Malternatives."