What you didn't take into account is that the thermal efficiency of a typical internal combustion engine is ~20-30%. While the thermal efficiency of a turbine generator can be up to 60%. So for given amount of fuel a turbine generator can produce 2-3 times the energy of a car engine. In the analysis you still need to take into account the loss due to the distribution of that electricity from the power plant into your car. But that should be relatively small and more offset by the increase in the thermal efficiency.