That number is what a contemporary Antiochene author, John Malalas, wrote down. It is unknown, however, how he reached that figure. John did serve the imperial government in Antioch, so perhaps he possessed some access to official estimates, but we should not imagine that the Romans were able to conduct a reliable survey of who died and who didn't. As we don't have any way to arrive at a better estimate ourselves, this figure is therefore extensively cited. I quote here the relevant passages from Malalas - even if the number he provided cannot be confirmed, we can get a sense of how a contemporary viewed the disaster and, with the help of other sources, how the imperial government responded to it, all of which combines to provide a picture of devastation and shock:

In the seventh year of his reign [Justin I], in the month of May, Antioch the Great suffered its fifth calamity from the wrath of God, during consulship of Olybrius. Great was the fear of God that occurred then, in that those caught in the earth beneath the buildings burned were incinerated and sparks of fire appeared out of the air and boiled anyone they struck like lightning. The surface of the earth up and foundations of buildings were struck by thunderbolts thrown those by the earthquakes and were burned to ashes by fire, so that even who fled were met by flames. It was a tremendous and incredible marvel furnaces, with fire belching out rain, rain falling from tremendous furnaces, flame dissolving into showers, and showers kindling like result consumed even those in the earth who were crying out. As a result Antioch became desolate, for nothing remained apart from some buildings beside the mountain.

No holy chapel nor monastery nor any other holy place remained which had not been torn apart. Everything had been utterly destroyed. The great church of Antioch, which had been built by the emperor Constantine the Great, stood for seven days after this tremendous threat from God, when everything else had collapsed to the ground during the wrath of God. Then it too was overcome by fire and razed to the ground. Likewise other houses which had not collapsed through the divine calamity were destroyed to their foundations by fire. In this terror up to 250,000 people perished. For this was the great festival of the Ascension of Christ our God and a great throng of visitors had come to town. During the wrath of God it became clear what a great number of citizens there was. Many of those who had been buried by earth survived to be brought up alive but then died. Some of the citizens who survived gathered whatever of their possessions they could and fled. Peasants attacked them, stole their goods and killed them. But God's benevolent chastisement of man was revealed even in this, for all those robbers died violently, some by putrefaction, some were blinded and others died under the surgeon's knife, and after confessing their sins they gave up their souls.

One who plundered at that time was Thomas, a Silentariuus, who had escaped in flight from the wrath of God and lived three miles out of the city at the place known as St Julian's Gate, and, by means of his servants, stole everything from the fugitives. He did this for four days, and as he was polluting everything he suddenly died though he had been in good health, and everyone glorified God. His property was stolen and lost. He was buried there, in the place where he died. Other mysteries of God's love for man were also revealed. For pregnant women who had been buried for 20 or even 30 days were brought up from the rubble in good health. Many, who gave birth underground beneath the rubble, were brought up unharmed with their babies and survived together with the children to whom they had given birth. Equally other children were brought out alive after 30 days. Many even more tremendous things occurred. On the third day after the collapse the Holy Cross appeared in the sky in the clouds above the northern district of the city, and all who saw it stayed weeping and praying for an hour. After the collapse of the city many other earthquakes occurred during the next 18 months. Buildings collapsed too at Seleukeia and at Daphne over a distance of some 20 miles. The emperor provided much money for the cities that had suffered. When he had heard of God's benevolent chastisement of man, he was afflicted with great sorrow; the games were not held in Byzantion and, when the time of Holy Pentecost came, he entered the church without his crown, weeping and wearing a purple cloak along with all the senators who also were wearing purple.