After a quick skim through that and his sources, I believe he has confused energy with electric energy.
Here's one of his sources, the GREET model of the DOE:
http://greet.es.anl.gov/results
I'm confident they don't confuse their basics, so I'll assume their summary graphs as fact.
They say the total energy involved in a conventional petrol ICE car is split about 5/6 pump-to-wheel and 1/6 well-to-pump.
Now, a litre of petrol is 9ish kWh - hence any energy expended to get it from dinosaur grave to pump is a bit under 2kWh. Converting l to gal you roughly get his 6kWh.
However, that's mostly nit electric energy. The tankers and trucks run on diesel. Heating stuff in the refinery won't be purely electric. Without accurately putting numbers on that, 6 cannot be the electricity consumption of the refinery if the total well-to-pump energy is 6. As Bender would say, does not compute.