Most air-tight houses have an integrated MVHR (mechanical ventilation with heat recovery) system, which is kind of the inverse of an HVAC setup. There's a constant small air current being moved through the house, and when it exhausts to the outside world a heat-exchanger captures as much heat as possible from the exiting air and uses it to heat the entering air. Airtightness means you can control where the air enters and exits, which means this trick is possible.
All that being said, I'd expect a permanently-installed stove to have a flue (which results in the stove technically being a leak, but that's solvable). I assume the kerosene stove mentioned above is in use while the house is incomplete, so not yet airtight.
