I’m on shaky ground correcting French, but I think that should be “c’est lui.” Moi, toi, lui,…

You are correct. To expand a bit:

French pronouns have four possible cases: as the subject, direct object, or indirect object of a verb, or not an argument of a verb at all. The declensions are:

je/me/me/moi

nous (colloquial: “on”)/nous/nous/nous

tu/te/te/toi

vous/vous/vous/vous

il/le/lui/lui

elle/la/lui/elle

ils/les/leur/eux

elles/les/leur/elles

In this example, the pronoun is not the argument of a verb, so the fourth case is used (moi, lui, etc.)

So it really is just a way for them to suck out the cash flow of Aramco and leave nothing but a husk for external investors?

Yes. Absent further evidence, this article is crap. It fails to incorporate the family-state-corporate nexus unique to Aramco.

Doesn't the portion of the dividend paid to themselves represent the amount they intend to spend on public services? I'm not sure it's correct to regard it as meaningless.

Sure, they could reduce government spending, or they could reduce the dividend, and reduce spending more, but in any case, the size of the dividend relative to cash flow or profits still says something about sustainability of the present course.

The KSA, after all, can't issue debt in its own currency, can it?

I think the point is simply if the dividend is paid to themselves then short of corruption or mismanagement they can always pump back that money into the company when needed.

Say you have a household budget, and you have separate "accounts" for different purposes.

If you pay money "to yourself" for groceries, sure, you can always take it back, but you still have to feed your family.

Writing down that your budget for groceries is $0 (or less than whatever is needed) doesn't give you additional freedom.