Well, I think that the Hittite civilization would probably have lasted quite a bit longer. I read somewhere the Hittites had quite abit of influence on Mycenean Greece, if Mycenean Greece still collapses, and the familiar Greek city states still come into existence later they would have a closer powerful neighbor to deal with in the Hittites.
Egypt may have done better with the Hittites still around, they were allies against Assyria, without the Sea Peoples the Hittites would still be there to balance out the power of Assyria.
Where this could get interesting is what that means for later civilizations. I would assume that Persia would still eventually arrive in the area. Would a check on Assyria power by the continued existence of the Hittites prevent the Assyrians from being conquered later, and would that mean Persia would have to conquer Assyria themselves instead of taking their former territory? Or would Assyria be stronger and able to resist conquest?
This could prevent the Greeks from as influencial, if the Phoenicians are connected with the Sea People, then they would not be around to trade with the Greeks and others. Would Alexander even arise in such a timeline?
Without Alexander there would be a huge impact on the Far East, India being the most obvious. Instead you could have a Persian conquest of India and perhaps then a much larger following of Persian religion. Maybe a sect of Zoroastrianism would arise that absorbed some teachings of Buddha..who knows.