The British take Al Hassa from the Ottomans early on, establishing a puppet kingdom there, and getting more interested in Arabia as well as very annoyed at Nejd for their relentless attempts to seize their lands on the peninsula. The British curtail many Saudi attempts to expand. By the time WW1 rolls around, the British have a large chunk of southern Arabia and are not interested in taking on too many new colonies/mandates in the region, especially considering that it is mostly desert and Britain already holds many of the peninsula's richest regions. Rather, they ally with Hedjaz, and allow its newly installed Hashemite dynasty to control the north of the peninsula as something in between an ally and a full blown puppet (so a quite loosely controlled protectorate). Nejd is not strong enough to conquer Hedjaz, especially not with Britain protecting them.
I might do a later map for this scenario just for fun. I'd imagine a sort of *Oman and *Yemen forming out of Britain's southern possessions, along with Kuwait and Qatar retaining their independence, a sort of "mega Bahrain" in the form of Al Hassa and the Trucial states either being part of Oman or independent. The Hashemite holdings and dependencies would likely coalesce into one kingdom. Zagros (which would gain Turkey's weird panhandle) starts off as an unstable federation, with Pontus choosing to stay independent and Armenia and Kurdistan getting locked in a war at some point when the country dissolves (communism may serve to keep it intact for quite a while if they fall under its influence, but eventually they are guaranteed to break up, probably in a bloody conflict). Expect at least a slightly bigger Syria, the rest of the world probably stays the same.