The first thing it would do would be to delay ocean, river and lake travel developmentally.
Humans used rivers as the earliest "roads" pretty much everywhere. With rivers being far more dangerous, they'd either wipe out the megafauna in them (more work than not), harvest them (less work than not), or avoid using the river.
Similar things would happen with seas and near-shore ocean creatures. Either humans wipe out the hostile creatures, harvest them for food and resources, or have to avoid sea/ocean going.
Assuming these hostile creatures aren't a net boon:
People's that didn't require clearing the waterways -- like steppe or plains nomads -- would have an advantage over the settled cities that rely on goods being transported by river, ocean or sea. So I could see "nomad" civilizations getting further ahead than (in our world) the flood-plain, and river/forest/coast civilizations (which started becoming more dominant around 6000 years ago).
Now, in our world, the nomad civilizations still tended to regularly conquer the water-dependent civilizations (often they where pushed by nomads further inland, and found the city dwellers rich and easy to conquer), especially early on in our history (Persia, for example, was a nomad civilization conquering a city-civilization originally).
Maybe this lasts longer.
In our world, eventually the city-civilizations started scaling up more. In the West, Rome, Egypt, Greece and their descendents start getting strong enough that they are able to usually hold their own against "barbarian" waves (at least until the Mongols). All of them, however, relied on water to do this. So I'm not sure how much it would help.
The other side of the coin, where harvesting this megafauna is a net benefit, is you'd see faster expansion of the city civilizations as they develop better ability to harvest it. Much like the mammoth fueled human expansion, the same could happen along the coasts of the world. It is possible that the land-based Nomads would arrive in an area and find it already harvested and fortified by the coastal peoples, slowing down their growth.
Learning deeper sea travel and being able to chase the great beasts of the water deeper would become a huge economic advantage. So naval technology might develop faster than it did in our world.
With most of your calories coming from the sea harvest, your base on land wouldn't need the land around it. Farming becomes less important. Fortifying yourself against raids from the relatively impoverished inland nomads becomes important. So you build your settlements on places like Venice, where a land army is at a serious disadvantage. Farming forests becomes key to producing the great ships needed for your food supply.
Maybe you go "a viking" and raid the land-dwellers for resources hard to find at sea, and force them to provide tribute or be crushed by marines. You battle with farmers, ensuring that large stands of forest you need for your ships stay intact.
Leaving sight of land remains dangerous for non-monster reasons, but you get better at it than ancient non-Polynesian people did in our history, because calories is power, and monsters are calories. Your ships scour the 7 seas for places to hunt the monsters and bring more food home. When you find monsters, you land and do the work to preserve the food, before setting out and heading home. Those places where you land become increasingly fortified, and eventually form permanent settlements, which rule over the local non-sea folk.
Advances in navigation eventually lead to global empires at lower technology levels than today.
Inland dwellers fear the coasts and the oceans, and have fragmented governments. Eventually those inland people develop better road technology, bridge fortifications strong enough not to be destroyed by the raiders. Eventually a the dryland war happens, where a large inland empire fights the largest ocean empire, and loses, but almost wins.
This causes a seismic shift in how the ocean civilizations treat the interior. Some attempt to clean out the rebels, others rule them, others start merging with them.
In this phase of history, perhaps the materials science of the drylanders and the astronomy of the wetlanders join, and they develop true ocean going ships, including coal powered iron clads. Around this time the deep oceans are no longer safe for the monsters of the deep, and an extinction event happens; the huge spike in food production followed by the collapse of the monster fishery leads to the wetlanders now needing dryland resources, and a massive war.
Ideally this war should be fought with airships, clockwork and lots of gears everywhere.