Not knowing the exact specifications of your electric heater it's difficult to give a clear answer.
No it isn't. The heat coming from the computer is
exactly the same per kWh as from a electric furnace.
You may argue that some of the power is wasted as sound waves, but even the sound waves will get absorbed by the walls and get converted to thermal energy. Moving air will collide with stationary air and generate heat as the flow calms down. Even the light from LEDs will get absorbed by the surface it hits and converted to heat. Every single milliwatt used by the computer is converted to heat.
The calculation is different for a heat pump (inverted AC), but a heat pump is not an electric furnace.
In practical situation, it is likely that they are extremely close to each other. In the OP situation, it asks for the electric cost which is the incoming energy to the house. It is possible that the electric energy go out from other wires such as the Internet wire.