I'm no map expert but it seems to use the same country outlines as this map from 1787. (It may even be the same map — the similarities are pretty exact in every respect; in which case it is just a translation of a British map.) Browsing other maps from this source makes it appear to me, anyway, that this is pretty standard practice for late-18th/early-19th century map making. Which is not too surprising since this is three centuries after the dawn of the age of exploration.

It is copied from a British atlas. This map is the world map from the Cedid Atlas Tercümesi, published in 1803. It is an adaptation of the General Atlas by British cartographer William Faden. More info about it here. The Wikipedia page about it has a ton of links to other webpages, articles, and papers about it.

PS, the MapPorn page, with tons of comments, is here.

Now I don't know how old this map really is. But important to note, is that the Orroman Empire lasted until 1922. So depending on when it was made it becomes less and less surprising.

This map is from 1630 by Henricus Hondius, which is very amazing. And also shows how little of Australia was mapped back then.

EDIT: My bad... missed the fact that you had written the year.

Anyhow it was most likely based on other maps. As the map form 1630 is already accurate it isn't that amazing that this one almost 200 years later is even more accurate.

The Ottomans had a pretty impressive cartographic tradition that went back centuries before this map. Ibrahim Müteferrika in particular was a cartographer of note. Check out this example by him from 1728

Also, keep in mind the Ottomans were building on a tradition of Muslim geography that went back centuries which itself stood on the shoulders of the ancient Greeks and Indians. Having such a deep understanding of what the world looked like was not unusual for them.