The author's calculations are for replacing the entire energy diet of the United States. He uses gross inputs to everything, rather than outputs and usable energy. He neglects any other storage capacity present in the country - no vehicle has any battery, no electrical device has any battery - and tries to calculate how much energy we need to store IF THE ENTIRE ENERGY PRODUCTION CAPACITY OF THE UNITED STATES DISAPPEARS ENTIRELY FOR A WEEK.
It's a nonsense calculation. The U.S. certainly isn't prepared today to go for a week without any electricity generation or even a single drop of fossil fuel burned, and there's no reason to demand that it be prepared to do so in the future.
The "findings" are akin to someone who says "The U.S. is borrowing a dollar a year. If we extend that to infinity, we find that the U.S. debt is infinite. PANIC!". They're nonsense. Have no meaning in the real world.
In the real world, one significant benefit of a widely distributed power generation infrastructure is that it won't all go down at the same time. The solar cells on your roof will keep generating electricity even if it's cloudy the next town over. And that means that the real-world requirements for a several-nines-reliability mostly-renewable energy infrastructure are several orders of magnitude less than what is being calculated here.