Would the Byzantine Empire basically be another Turkey or would it be on something different? Is it going to participate in World War 1? If yes, on which side? What impact might it have on international politics?
Minimalist change may be that in 1201 when Alexios IV Angelos was getting smuggled out of Constantinople, he gets killed instead. Which prevents the Crusaders from coming and sacking the city and leaves the empire not split up by the Crusade. Which allows for a reconquest after the Mongol invasion on the Sultanate of Rum in 1243.
History really starts diverging by 1300 as the empire would be united and much richer; which would greatly change the ability of the Ottomans to conquer them/rise to power. As the Ottomans were a great power which had a large amount of influence on world politics it would become increasingly impossible to guess how things would have turned out.
Their is an assumption that the Renaissance may not have happened or have been delayed due to the existence of the Empire; that may be valid, but it is also possible to say it still happened as the merchant states of Italy were already very powerful by 1201 and scholars may have copied the books from the intact libraries of Constantinople.
If one wants WW1 to happen then it seems that one could treat the empire as though they were the Ottomans in world affairs. Now relative to religion that is a problem, so having the Mamluk Sultanate continue to be a major power, as well as Persia, might be something to consider. As for what side of the war they would be on, that would depend on a lot of factors so one could choose whichever side one desired them to be one for one's purposes.
Of course, that is just one point that appears to have made a difference, it is easy to argue that it wouldn't have made a difference or that a different place/time would be better. There are certainly other points from which it might lead to a much stronger empire, but that would make it harder to argue that the rest of the world developed as we know it to lead to WW1, in my opinion.
The long term survival of the Byzantine Empire is going to make a lot more changes than simply wondering if they will participate in WWI.
As a very simple example, one of the drivers of the growth of the Serenìsima Republic Vèneta was the decline of the Byzantine Empire and the opening of opportunities for sharp Venetians to dominate trade links to the end of the Silk Road. The crusades and the growth of Islam would certainly be far different with a thriving Byzantine Empire in possession of Anatolia and the Middle East, and Russia's history would also have no references to the Moscow becoming the "Third Rome".
Going even deeper, one of the drivers to trigger the Renaissance was the scholars fleeing Constantinople with copies of ancient Greek and Roman manuscripts in advance of the Islamic armies. With the knowledge of the ancient world locked away in the vaults of the Byzantine Empire, it might take much longer for Europe to move past the Middle Ages. It would also keep the "centre of gravity" for Western civilization firmly in the Eastern Mediterranean sea, as it had been since antiquity. Maritime powers like England or the Hanse would remain peripheral powers, and most likely beholden to the Byzantine Empire for fashion, intellectual leadership and political and economic power.
And of course, the Byzantine Empire would be a constant challenger to the Catholic Church and the power of Rome. The possibility of religious wars between the Catholic and Orthodox churches would certainly bend history all out of shape.
So the question is essentially unanswerable in its current form.