It is disappointing, but understandable, that he feels the need to make methane in general seem more irreplaceable and vital to human happiness than it really is.
And in the end, it only solves cooking. Electrification solves many more problems at once, and notably refrigeration.
Much of the extant Third World is in its Third World-ey condition because of abysmal governance. That is usually accompanied by infestation of power and grid companies by grandnephews of top politicians etc.; those companies handle a lot of money, are highly centralized, and are thus a prime target for graft.
The bizarre story of South African ESKOM and poisoning of the director who was asked to reduce corruption comes to mind. [0]
[0] https://yris.yira.org/interviews/by-not-speaking-out-when-so...
A country with a well-functioning grid is probably already on its way from poverty.
The 3rd world is much better off switching to solar. With an induction hob you can probably get away with 1000 Wh / day. A 200W panel, a 1000Wh battery, a 1500W inverter and a 1500W hob would cost around $500 and last 20 years. It can also keep a cell phone charged or used for refigeration instead or ...
OTOH, a propane burner might cost $20, but then you'll be spending $10/month on propane, and are super vulnerable to being cut off from your source.