>It's kind of surreal to use "Saudi" as the demonym for the people of Arabia

Huh? They use it as a name for "people from Saudi Arabia" and it's a very common use.

"some users of Saudi nationality or descent live outside of Saudi Arabia" --> people who are SA nationals/origin and live outside the country.

>The "Saudi" in the name of the country refers to the royal house, the House of Saud, and I would expect a "person of Saudi descent" to be Arabic royalty, not just any old Arab.

Saudi != Arab. If anything, Arab is a superset (and Saudis, if we talk about the nation state and not the ethnicity, are not all Arabs).

But the main point, is that the name Saud is commonly used for the nationals of Saudi Arabia, not just the royals.

Wikipedia: Saudis or Saudi Arabians are a nation composed mainly of Arab ethnic groups who are native to the Arabian Peninsula and live in the five historical Regions: Najd, Al-Hijaz, Asir, Tihama and Al-Ahsa;

Arabia is a peninsula. Qataris, Yemenis and Emiratis among others would not appreciate Saudis attempting to appropriate Arabian to refer to those from Saudi Arabia.

And Arab refers to people from Morocco to Iraq so it’s equally unsuitable.

Exactly, imagine if people of the United States appropriated the name 'American'! I'm sure that every other country in the two Americas would be up in arms!

(It is a joke, laugh).

Some other countries actually use terms like United Statians or North Americans. And after traveling a bit makes the USA's use of 'America' seem arrogant or ignorant.

In italian "statunitense" is used, but probably not as often as "americano".

Canadians might still not be pleased about 'North American'.

I'm guessing you haven't traveled much. American is a virtually ubiquitous term to describe someone from the United States worldwide, no matter which language you're speaking. Countries which have a problem with calling yourself American are a minority, and even then it's usually a small minority of the younger generation.

If you go anywhere within Latin America, you'll find quite quickly that "American" is used to describe someone from the continents, and it's consider very odd to introduce yourself as "American" to a local. You say you're Estadounidense, or "Soy de Estados Unidos" (From the United States).

It's actually a very charged topic in Latin America, as many latinos feel that the word they use to describe themselves has been stolen.

I’m sure every other country with America in its name would be.

well, the complain was about calling Arabs the people from Saudi Arabia.

It was a bit of sarcasm, as it is exactly comparable. Go look at a globe and tell me which other countries have “America” in their name ;)

There are other Arab countries. Most people know what is meant by "Saudi" even if it's technically not correct

It is technically correct, although not official.

Wikipedia: Saudis (Arabic: سعوديون‎ Suʿūdiyyūn) or Saudi Arabians are a nation composed mainly of Arab ethnic groups who are native to the Arabian Peninsula and live in the five historical Regions: Najd, Al-Hijaz, Asir, Tihama and Al-Ahsa;

I think they just mean expats, or dual citizens, or Saudi Citizens living in the US. I don't think they meant the Arab ethnicity.