Someone already invented it [minus the useless electrical part], http://www.kellykettle.com/
They've been around for years in one form or another, we were boiling water in one 60 years ago.
Alternatively make one yourself using a perforated metal sleeve, like the armed forces did in WW2.
Given the energy required to manufacture a Biolite
, the amount of use the average camper would give it, they'd generate less Co2 by sticking to gas/petrol.
Whole thing is a triumph of style over substance imo.