Eventually, Alexander would have been thwarted. He would have spent the rest of his life defending his empire against enemies real and imagined, both within the empire and without. Perhaps he would have pushed his frontier in India as far south as the Ganges or even further, but sooner or later (and probably within his lifetime) he'd be beaten back to the Indus and beyond. In Arabia, no doubt he would take the Hejaz, Hadramaut, Yemen and Oman, leaving only the empty quarter unconquered. he may even cross the Red Sea to engage Aksum or whatever Ethiopian power is there.
His aborted attempts to press Westward might lead to the development of a Modus Vivendi between Carthage and Rome, perhaps avoiding the Punic Wars and allowing both to expand together, even resulting in both lasting longer than they did because of their ability to defend against Barbarians (How about, for example, Carthage becomes mainly a naval power, while Rome becomes mainly a land power, with each others' spheres negotiated and sacrosanct?)
Meanwhile, Alexander is going to be holding on to his own empire as he fights of rivals from the North (Scythians, Yuezhi etc.), from the South (Indians, East Africans, and perhaps Ethiopia and Meroe), from the East (More Indians, Tibet, more Yuezhi, Huns, Turks etc.) and from the West (Rome and Carthage). Perhaps his dynasty lasts longer if he survives, and there is an Iskandrid dynasty in the Persian Empire, but I can't see this leading to a world-spanning Macedonian Empire.