Back when I had a class in power engineering as part of my EE program there was about a week discussing transmission line loss. The example we worked on was Hoover Dam which sends its electricity 266 miles over transmission lines to LA where the University was. It was remarkable how much energy was lost both in what are called "i2r" (I squared R) losses (that is just the transmission wires losing energy as heat) and radiation losses where the power lines are essentially very long antennas. There are lots of strategies that are employed to mitigate both kinds of losses, those strategies have their own limits as well. It is all rather more complex than just hooking a wire from point A to point B, as such things are.
The other advantage that Casey's scheme has is power generated during the day doesn't need to be consumed right away if it is stored in Methane. This is true of Nuclear power as well.
The efficiency argument weakened still further if you compare the full cost of drilling, extracting, transporting, and then burning existing "fossil fuel" sources of methane because that not only damages the environment with the contaminated ground water from fracking or other extraction methods, but adds to greenhouse gasses in the the air.
The efficiency here is that your take zero (or nearly so) carbon foot print energy generation to create fuel that has net 0 impact on warming gases in the atmosphere (it takes the CO2 out of the air which is then re-released back into the air when it is burned). For things that can't be electrified, or are better served by heat combustion. Those things are, jet fuel, heating homes, baking, etc.
The other advantage is it re-uses existing infrastructure. So on a dollars per ton reduction of CO2 it is much more efficient than existing solutions, whether you use solar or nuclear.
Like most things, efficiency is a measure of some metric with respect to two choices to achieve the same result.
The choice presented by Casey is "How do you get methane for things that use it?"
If your metric is greenhouse gas emissions you get more gas with has a much lower greenhouse gas impact. On that basis it is much more efficient whether you use Nuclear or Solar as your energy input.
