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Most of the factions you'll find in game are in fact 'Turkic', not just the Sultanate of Rum or the Great Seldjuks but also the Khwarezm Shah or the Ghaznavids. Turkic here meaning that at least the upper strata of the ruling class was of Turkic origin. The original first Seldjuk empire was that which you may label the Great Seldjuk Empire which rose to prominence in the 11th century. Mind you it was not the first, the first Turkic muslim realm in fact was the
Ghaznavid Empire, which took over the Persian Samanids in the late 10th century. Before the 11th century the Turkic peoples had been used often as ghulam soldiers by the Caliphate. As central power broke down they eventually stepped in and as the strongest military force around and seized forcefully the reigns of power. Mahmud the Ghaznavid displaced his Persian masters and quickly expanded his borders. Amongst the clients of Mahmud were the Ghuzz Turks from the Aral Steppes (called after the semi-mythical ancestor of the Seldjuks). They were a quarrelsome clan of adventurers, jealous of each other yet always apt to unite in face of a common foe.
When Mahmud died in 1030 they rose up against their former masters and drove the Ghaznavids out of Persian into their Indian domains by 1040. The senior member of the clan, Tughril Beg, made Ispahan his capital in 1050, leading an empire including Khorasan and Persia. In 1055 they entered Baghdad at the invitation of the Caliph who was fearful of his Turkic minister intriguing with the Fatimids. The Abbasid Caliph now proclaimed Tughril 'king of east and west', as such all temporal power in what was technically the remnant of the Abbasid Caliphate now fell to the Seldjuks.
Both the Byzantines and the Fatimids throughout the early 10th century had found an equilibrium that clearly divided there spheres of interest. They would not always be in accord, but in general they didn't wish to confront one another. The reason was amongst others the emergence in the east of the Turkic danger. For both the Byzantines and the Fatimids it was real enough, for the latter there was of course the fact that the Seljuks were Sunni and backed the Abassid Caliph against the Shia Fatimid Caliph. Turkic raids into Anatolia date as far back as Emperor Basil II when the Ghaznavids still were nominal overlords of the various tribes. The response of the Byzantines was to annexate piecemeal all their Armenian buffer-states. As Turkic power extended, so their raids became ever more frequent. Tughril took part in only one raid himself in 1054 which devastated the lands around Lake Van but failed to seize the fortress of Manzikert. Usually the raids were led by his cousins Asan and Ibrahim Inal. For the Great Seldjuk Empire, the enemy were not the Romans but the Shia Fatimids.
When Tughril died in 1063 his nephew and successor Alp Arslan was more anxious to secure his western border, since he was concerned about a possible Byzantine-Fatimid alliance. Before venturing to defeat the Fatimids he wished to secure his flank by incorporating Armenia into his empire and thus neutralising the Byzantines. From 1065 onward Edessa was attacked yearly while each year saw new and devastating raids into Roman lands, seizing Armenia by 1067. The Emperor could not ignore this challenge any longer and set out with his army.
I don't need to explain Manzikert
Alp Arslan was thus contented. Byzantium was bested, its army destroyed and his western border secure. He had no wish to conquer Anatolia for the great Seldjuk project was always the unification of islam for the Sunni adherents. The number of the Fatimids was now up... not that Arslan himself would ever see that pass, he marched off on a campaign in Transoxiana were he died in 1072. His son and successor Malik Shah, like his father, had no personal interest in Anatolia so he commanded his cousin, Suleiman ibn Kutulmish to conquer it for the Turkic people. The Turkic invasion of Asia Minor eventually began in earnest around 1073 in a series of invasions that were neither uniform nor concerted. It was spearheaded by lesser princes of the Seldjuk clan, men like Danishmend, Chaka or Menguchek who had no immediate future in the Great Seldjuk Empire as lesser scions in a greater house. Thus they set out to carve out lands for themselves in the Roman lands, now open to them. Backed by the Great Seldjuks of Baghdad and Ispahan, the Seldjuks of Rum gradually conquered large swaths of land.
So the Sultanate of Rum as the game shows was in reality not that united as it may seem. After the death of Malik Shah the Great Seldjuk Empire itself began to face a decline which rendered their overlordship over the Seldjuk 'family' increasingly nominal untill eventually it was only in name that they were the 'great cousins' of the Turks in Rum.
I hope that more or less explains it.