If you don’t close the box of the system at some point to isolate the input, efficiency would be meaningless. I think in the context of the original post, suggesting running a server in winter would be a zero-waste endeavor if you need the heat anyway, it is perfectly clear that the input is electricity to your home at a certain $/kWh and gas at a certain $/BTU. Under that premise, it is fair to say that would not be true if you have a heat pump deployed but would be true compared to gas furnace in terms of efficiency (energy consumed for unit of heat), although not necessarily true economically.

Generating 1kWh of heat with electric/resistive is more expensive than gas, which itself is more expensive than a heat pump, based on the cost of fuel to go in

If your grid is fossil fuels burning the fuel directly is more efficient. In all cases a heat pump is more efficient.

I think this is pretty silly either way.

- There's an upstream loss on electricity directly in proportion to how much you use; ignoring this tilts the analysis in favor of electricity.

- You pay more for heat from electricity than gas, in part because of this loss.