Some thought that … and some didn’t. Some noticed the shape of the Earth’s shadow on the Moon was round. Some noticed that as ships sailed into the distance, they ‘sank down’ until only the sails were visible. All ‘people’ weren’t smart about it.
Anyway, putting a big map like that on a 6-foot globe, you could stand in one place, spin it, and see it all.
Related fact: the Greek astronomer Anaxagoras taught that the Earth went around the Sun … 1500 years before this map was made.
I ran across the unglobed map before I found the planisphere at the online British Museum’s ‘Silk Road’ exhibition. Go there and look for the text ‘Map of the world from al-Idrisi’. https://www.artnews.com/art-news/news/british-museum-silk-roads-exhibition-1234722468/
I found the planisphere image on the Wikipedia page for ’ Tabula Rogeriana’, which shows several chunks of the map. (Idrisi maps all have ‘South’ on the top of the map.) In the ‘significance’ section, there’s a big version of the map. None of them are maps of the whole Earth … it’s said that his maps were all based on what people who’d been there told him.