They didn't exactly go back to being tribal.

I want to address the inference that can be made from this:

it had devolved back into tribal society

Characterizing the transformation of a society into a tribal one as devolution is subjective. You can argue it's a social devolution, but you can also argue it's an evolution depending on one's perspective. Tribal people tend to view their form of social organization as better than, if not superior to, non-tribal people. Non-tribal people, on the other hand, tend to view their form of social organization as better.

People in seventh century Arabia can be divided into groups: nomadic and sedentary. Tribes, by definition, were politically independent. As states arose that could establish control on urban centers in Arabia, sedentary tribes lost autonomy and were effectively subjects of whatever state was ruling over them; people became more of town residents subjected to state laws and regulations and less members of a tribe. This saw no reversal. The nomads, on the other hand, having been beyond state control escaped this. They had continued to live in tribal groups into the twentieth century.

Societies in the modern history of Arabia tend to be described as predominantly tribal and nomadic, but that's really just an unfortunately popular misconception. Speaking about the formation of modern-day Saudi kingdom, Madawi Al-Rahseed, in A History of Saudi Arabia notes:

it is surprising that the Sa'udi state is still mistakenly considered by some scholars as the epitome of the tribal state. This misconception continues to be propagated despite evidence to the contrary. While substantial sections of the population were certainly tribal in the 1930s, the state was definitely a non-tribal entity that gradually undermined and broke the cohesion of the various tribal groups.

The problem with the question is that it presupposes that during World War I the Middle East was a coalition of ‘tribal’ leaders. This was not the case all as a previous answer has demonstrated.

To answer the substantive part of the question- how did the single Arabic Empire of the early era no longer be around by WW1, will have to be gone over in the briefest details. Since to answer it one post is summarising many centuries of history of the Middle East, most of it incredibly detailed and somewhat complicated; what follows is the simplest possible illustration.

Please note- while your question asks specifically about the Arabian Peninsular one cannot discuss that region isolated from the political centres of the Islamic world.

The idea of all Muslim lands being controlled by a single power was the model used by both the Rushidun Amirs, the Umayyad Caliphate and the Abbasid Caliphate. This should not suggest it was entirely unified by consent. From the era of the first Fitna (the name given to the first of many devastating civil wars within the Dar al-Islam) and onwards, the vast and growing empire was riven by ethnic, religious and political differences.

For example, we had the Umayyad dynasty face rebellion in the form of the fanatical and extremist Kharijites; after the murder of Ali ibn Abi Talib you had his supporters in Kufu politicise their veneration of him, leading to the development of the party of Ali (the Shi’a); you had tension between the more polyglot and cosmopolitan Umayyad and hard line Arabs under Abdullah ibn al-Zubayr (and the suggestion with it that his forces represented most of the Arabian peninsular) and eventually you had the black flag bearing Abbasid’s who toppled the Umayyads and became Caliphs.

It was this act that led to the first fragmentation of the supposedly unified Caliphate. The Umayyad dynasty fled Syria, relocated to el-Andalus and declared an alternative Caliphate based in Córdoba (eventually becoming the Emirate of Córdoba). By 969 you had the Fatimid Caliphate rise in Egypt and North Africa.

One had become three.

The Abbasids may have overseen the Golden Age of Islam, created a magnificent capital in Baghdad and laid the seeds for kick starting the renaissance in Europe some centuries later, but political power began to diminish as the decades passed.

The Caliphate faced trouble with ‘barbarians’ in their borders (in this case the Turks), who began converting and dominating politics both within and without the Empire (so you have the ‘very proud we are Muslim’ Ghaznavids waging war on Turkish mamluks fighting for the Caliphs). In time it led to increased fragmentation of the lands under the Abbasids.

Thus you had the rise of what could be described as states within states, as either a) factions within the Caliphate carved out their own territory while nominally being loyal to the Caliphs or b) outsiders came in, nominally converted to Islam and kinda helped themselves.

So you see the Iranian based Sassanid venerating Buyids in 934 take over huge parts of the Caliphate and the Turko-Persian Seljuk’s invade and carve out an Empire around 1075.

With the destruction of Baghdad by the armies of Mongols in 1258, the idea of a unified Dar al-Islam faded, seemingly forever, and the Middle East really became a bevvy of smaller states whose rise and fall over the following centuries is fascinating. But at no point could they be considered to have ‘devolved’ into purely tribal states.

When we get to World War One however, the Ottoman Empire has been in charge of the region for centuries. And while the Empire was in decline compared to where it had once been, it was still firmly in control of the Middle East. As stated above, the region was not tribal whatsoever; rather it was part of a continent spanning Empire who ran it rather efficiently.

This is it to say that there were not ethnic/tribal conflicts. There were. And these often led to rebellions. Yet the Ottoman’s were able to crush such things quickly and their efficiency at doing so, coupled with their willingness to transport large numbers of traibesmen vast distances across the Empire to prevent them returning (such as the movement of large numbers of Libyan Arabs from their homelands to the region we now call Palestine/Israel in 1784), again meant that the region could not be considered a series of ‘tribal states’.

It was these long standing regional resentments towards the Ottoman’s however that the British and French sought to exploit during World War One.

Crucially, the Arabian peninsular came under the domination of the House of Al-Saud during the aftermath of this but this was also not facilitated by tribal alliances, more the effectiveness of the fast moving militia, the Ikhwan, who were organised outside of tribal lines, being motivated far more by strict Hanbali Islam and the teachings of Muhammad ibn Abu-al Wahhab.

This is of course only the briefest and simplistic of summeries; you are talking about roughly 1200 years worth of Middle Eastern history here and I am afraid only a snapshot is possible.

Two excellent popular introductions to the vast scale of the history of the Islamic world which I heartily recommend for those new to this field would be ‘Destiny Disrupted’ by Tamin Ansary, or ‘A history of the Arab People’s’ by Albert Hourani.

Both do an excellent job of introducing and explaining the complicated sequences of events both political and intellectual across the centuries.

I would also recommend ‘The Ottoman Empire 1300-1605’ by Colin Imber; which contains incredible detail in how the Ottomans ran their provinces (while it ends some centuries before WW1 it is an excellent guide to the local politics of the lands in question) and ‘The Fall of the Ottomans’ by Eugene Rogan for an account of the period you enquired about.

(Forgive any formatting issues here; this post was composed upon a phone while travelling).