If you think it as a battery of a fuel cell, you care about the voltage and the charge, not about if it has Lithium or not. In general in the redox reactions (and in batteries) you don't care too much to which atom the electrons are bound (unless you have to build one). So the electrons are the important thing and the molecules are the implementation detail.

> What we are doing is taking in matter with a certain amount of chemical potential, putting out matter with less chemical potential, and capturing the difference. Electrons are intimately involved in this, but they're a bit of an implementation detail.

You are totally correct too. :) It's equivalente to the previos point of view where the electrons are the important part and the molecules are the implementation detail. It is just that sometimes it is easier to think from one point of view and other times it's easier to think from the other point of view.

(Essentially, Volt = Energy / Charge. Since the charge of the electron is fixed, you can convert easily (or use eV to measure the energy).)

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If you think about the methane as a charged battery and the carbon dioxide as a discharged battery, then the idea is that the high potencial electron comes from the food and go away as low potencial electrons in the breath. I'm not 100% happy with this analogy, I think I understand it, but I'm not happy. You are not accumulating electrons.