If not Manzikert, the same thing would have happened in the next battle, or the one after it. Besides this, it's irrelevant to the point that the levies of Byzantium are probably too high. They should not be able to overpower the Turks in Anatolia at game start in 1187 with almost double their troops.
"As the below table demonstrates, the population of Byzantium did not fall as a result of Seljuq acquisitions; manpower was still as readily available in 1143 as in 1025. In fact, Western Asia Minor and Greece experienced a population growth on an unprecedented scale, thanks in part due to the trade of the Italian city states of Venice and Genoa and also due to the influx of Greek refugees fleeing the Seljuq Turks.[45] Manuel Komnenos' first expedition to Konya saw the entire Greek population of Philomelion evacuated and settled west. However, the efficiency and resources needed to raise large armies had dwindled somewhat, as can be seen by John and Manuel's failure to create a national army.
Year Population Soldiers Area
1025 12,000,000 250,000 Byzantine Empire
1143 10,000,000 80,000 Byzantine Empire
1204 9,000,000 30,000+ Byzantine Empire
1281 5,000,000 20,000 Byzantine Empire[46]"
And if we're talking strictly from the viewpoint of game balance, Byzantium seems to be okay in the hands of the AI. It's hit-or-miss.