You are right, of course. These folks had no idea that they lived on a huge globe. "The world" was most likely defined as what could be seen from horizon to horizon.
I do not doubt that there was a great flood. There have certainly been many great floods on planet earth in my lifetime, and to the people who survived, their world was destroyed.
In the absence of satellites photos showing the boundaries of the flood, I am certain that people affected by huge floods believed the whole world was impacted.
And the survivors told the stories. Oral tradition takes on a life of its own. I tell my 5 year old stories of events in my life, and I am always surprised how she embellishes them, adding in heroic details that were never in my original telling.
So these folks told stories around the fires in the evening, generation after generation, of some guy who saved his family and some farm animals from a great flood. And the children hear the story year after year, and when they grow up to tell the story themselves, some details get left out, and other, fantastical details get added in, and the next generation embellishes more, and the next generation more, and by the time that somebody literate gets around to writing the story down, it has become bigger than life.