Statistically, the political survival of a ruler (defined via the probability of being ousted in the next two-year period) in an autocracy is significantly higher than in a democracy. That is, an autocracy is statistically more stable than a democracy.

The bolded part isn't using the same meaning of "stable" as most comparisons of forms of government. Most people are usually concerned with the stability of government institutions as a whole (because they provide services like public order, support the economy, etc.). So while a western-style democracy may be less "stable" for the ruler, change of ruler is much less likely to screw the institutions, compared to places like North Korea, or pre-revolutionary Libya.

The most stable autocracies are those where the ruler doesn’t need people as a source of resources for rewarding his coalition of essentials. For example, when a ruler has oil he doesn’t need to extract taxes from the populace, which means he isn’t compelled to provide public goods and policies that increase tax income, which in turn means that he is free to suppress his people in order to minimize the chances of a successful revolution.

The bolded part looks really fishy - how does providing public goods increase income? (I mean, it might increase it as bit, but not as much as the expense of public goods).

A more plausible explanation (that fits better with the rest of what you wrote!) would be that extracting money from a large population requires a big organization, many parts of which may revolt (so they are "essentials"), whereas extracting money from some oil fields requires a much smaller group of essentials.