Part 1

Your question is a good one, but I wouldn't take this video too literally.

These types of videos are popular, but they reflect a view of states and borders that is deeply anachronistic and that suggests that concepts like statehood and borders that we're familiar with today would have been the same throughout history. They were not. They also tend to be entirely arbitrary in what is or is not a state and in how they define what these territories are.

That's even before we get to flat out inaccuracies. (To give just one, the Sharifs of Mecca declared allegiance the Seljuks and the Abbasid Caliph in 1070 as is reflected in the video, but they resumed allegiance to the Fatimids from 1074-81, which is not.

That example points to the kind of problem in creating a "state control map" has in the Middle Ages. The Sharifs of Mecca were no more or less de facto independent from either the Seljuks or the Fatimids between 1070 and 1081. The Sharifs of Mecca originally pledged their allegiance to the Fatimids entirely voluntarily. Their allegiance to the Seljuks, on the other hand, was purchased with an annual pension.

Notice that at no point is the actual situation reflected very well in the video, which is that the Sharifate of Mecca was de facto autonomous and under the control of the same broad dynasty for most of the 1000 year period from the 10th century to the 20th. The extent of outside "control" for most of that period was limited to the suzerain's name being recited at the Grand Mosque of Mecca each Friday and whatever armed expedition was sent to accompany each year's hajj caravan. While at various periods the outside powers controlled the appointment of the Sharif, once in power they were virtually left to their own devices.

The "loss of control" in 899-900 is similarly illusory. The fact is that communications with the interior of Arabia were so poor that there wasn't much state control of central Arabia in the Abbasid period at all.

That of course requires some discussion of what a state is and what a state does, because that lack of control of the Arabian tribes is a feature that distinguishes certainly the Abbasids from the Rashidun Caliphs and to a certain extent from the Ummayads. This early period is somewhat opaque to us and I'm heavily generalizing, the early Islamic Empire was an Arab empire that relied on the manpower of the tribes in order to carry out the conquests. In a sense we can think of that early state as having control over the tribes in somewhat Feudal terms, as they were often linked by marriage with the leadership and were a key element in the campaigns. Already by the time of the Ummayads and certainly by the time of the Abbasids that that had ceased to be the case. Some view that shift in the empire from one centered on Arabia to one centered on Egypt/Syria and then on Iraq as being the essential cause of the succession struggles in the first place as the empire struggled to define its identity. Without getting into all that, by the middle period of Abbasid rule, Arabia in general was not a political, military, or economic center of the empire. The tribes, including those of central Arabia, neither demanded much from the central empire, nor was much required of them.

That's one reason why this map, even on the more populous coasts of Arabia, tends to only change when some group emerges that causes problems or otherwise rebels in such a way as to compel an outside response, as in the appearance on the map of the Qarmatians in 899, which seems to be what prompts the map's creator to decide that the Abbasids were no longer in control.

That of course is relatively normal for nomadic tribal societies on the peripheries of settled empires. It's my understanding, for example, that our knowledge of Germanic tribes in the Roman period is largely limited to the history of tribes that either attacked Rome or that were attacked by Rome.

In the case of Arabia, we might know the names of the tribes, their grazing areas/territories, but "states" in most of Arabia are historically abnormal. This requires some framework for what a "state" is, but if we assume, for example, that the Prophet Muhammad created a "state" (itself very much a deeply contested assumption) then his appears to be the first such state on the Arabian peninsula except for the Kingdom of Yemen.

Without getting overly philosophical, however, our entire historical concept of "The State" was invented to describe conditions in Europe that are often merely analogous to conditions elsewhere, and that are often very poorly suited to describing conditions in tribal societies. Nomadic and semi-nomadic tribal societies are in some senses antithetical to the existence if not the concept of states. Most states that have nomads within their borders have, in the past 200 years, undergone some sort of effort to permanently settle them. This was true of Russia, the Ottoman Empire, the Turkish Republic, the Persian Empire, The United States of America, and elsewhere.

In areas that are the sole domain of such tribes, as in the interior of Arabia, the terminology of "state" is perhaps even less apt. In what sense, for instance, was the first Saudi "state," the Emirate of Diriyah any less or more of a state after the Saudis began their effort to gain hegemony/suzerainty over Arabia?

In a Weberian sense, did they exercise a monopoly on the legitimate use of force? No. To borrow Fred Donner's definition in looking at the early Islamic State in the 7th/8th century, did they have: "[a] set of political institutions resting on a conception of legal authority; the institutions considered relevant are (a) a governing group, (b) army and police, (c) a judiciary, (d) a tax administration, and possibly (e) institutions to implement state policies other than taxation, adjudication, and maintenance of control by the elite."?

To the extent that this existed anywhere in Arabia before the 20th century it was limited to the most prominent cities.

In Tribes and State Formation in the Middle East the authors discuss this problem of defining the state in the Middle Eastern context, particularly in contrast with or in the context of tribal societies. Richard Tapper, for instance writes that "the existence of territorial frontiers (however vaguely defined), a central government (however weak and limited in its aims) and a heterogeneous population, are enough to define the state. In these terms some confederacies [of tribes] constitute states, while some states operate on the basis of tribal ties, or, in the form of empires, recognize the autonomy of other states and tribes within their territories."

This goes both to the core of the question and to why the video is so misleading. Under this definition we might say that what distinguishes the Saudi states is their ability and goal of forming heterogeneous confederacies under their chieftaincy and thus expanding their territorial control even if that territory is incredibly vaguely defined.

All of that is one incredibly long preface in trying to answer your overall question about what was happening in central Arabia in 900-1744.

There are multiple ways to go about answering that. One answer is "we don't really know." Because there was so little engagement between the tribes of central Arabia and the outside world we have very little information about them in general until the 18th and often until the 19th century. When we do get information about them it's often in the context of groups that have that outside context. So for example, what we know of the Otaiba tribe of the eastern Hejaz and souther Najd is often limited to where they stood in the various conflicts between the Sharifate of Mecca and the Saudi states.

Another answer would be to take an anthropological or ethnographic approach. The Anaza tribe of the northern Najd (of which the Saudis are part) might not have been "doing" much politically in terms of state formation, outside diplomacy, or outside conflict, but that is in, fact, "normal" for Arabia's history, so instead we might look at how their society functioned, what their grazing territories were, what the geography of that territory was, etc. Answers to those questions, happily, can also take advantage of "longuee durée" history. If camel-herding tribes went up a particular valley in winter and came back down it in summer in 1910, we can be reasonably certain that they would have done exactly the same thing in exactly the same spot in almost exactly the same way 500 or 1000 years before, or even back to the domestication of the dromedary camel 5000 years ago.

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I'm running out of characters so I'll attempt a conclusion in Part 2.

[edit]: Accidentally got my part numbers wrong :)