It's not about fault at all - I'm just saying that the analysis does not apply to lightbulbs. For a lightbulb to be as efficient as a resistance furnace at heating a room, you would need to have zero light escape that room so that all the light would be converted to heat. Then, the heat would leave the room at the same rate as heat generated by a resistance furnace.

Even if we consider incandescent light bulbs, which waste most of the energy they use as "heat", that heat is actually being transferred primarily through radiation, so it can escape through windows more easily than the heat that a furnace transfers to your indoor air.