Hah, I saw that thread over at /r/mapporn but was on my mobile so I couldn't respond.

Unfortunately, while I know Ignaz Hatsek as the great Imperial mapmaker of his time I am not sure how exactly he came to these numbers.
I don't have immediate access to the complete 1880 census but I do have access to the Austrian National Library's magazine archive, which includes the "Statistische Monatsschrift der k.k. statistischen Central-Commission", a monthly statistics magazine in existence from 1875 to 1921.

Looking at the 1881 collection, which includes both the complete population statistics and various articles referencing data from the recent census, there is only one article that might be relevant here: "Die Volksunterrichts-Anstalten [public schools] in Bosnien und Herzegovina im Jahre 1879" by Berthold Windt.

In 1880, Galicia actually had the second-highest total absolute number of people trying for an admission (2,417) to a Gymnasium (secondary school towards uni) after Bohemia (3,798) with an average amount of rejections. Although for the Realschule (trade school) the numbers were abyssmal at only 182.

The Austrian and Bohemian crown lands had a compulsory 6-year education in place ever since the Empress Maria Theresia. Hungary as well but a bit differently.
When Galicia became a Habsburg possession in 1772 after the First Partition of Poland the population was almost exclusively a tiny upper class of Polish aristocracy and their serfs, similar to Russia. Education was almost nonexistant for the majority and the only work was working the fields with outdated and low-yielding techniques.

You wouldn't believe it from the map but under Habsburg rule things got much better. When the enlightened Joseph II. followed his mother on the throne in 1780 he tried to encourage German farmers and industrialists to settle over there with large subsidies of land and tools, he allowed protestants free practice even before he did in Austria proper, he founded Galicia's second university (after Krakow), the Lemberg university, in 1784 and generally did his best to improve the situation in the province.

Unfortunately, Galicia only introduced compulsory education as part of the complete re-reforms of 1867. As a result, the main drive to educate the children came from priests and teachers, but especially during seeding and harvest times the kids were needed on the fields and so only sparsely at schools, if at all. Smaller villages only had basic schools anyway and if the parish was too small you wouldn't even get a teacher, although many communities tried to work together and have literate members try and teach the local kids basic skills during the boring winter months.

Sources:

• Beales, Derek - Joseph II: Volume 2, Against the World, 1780-1790 (ISBN 978-1107616264)

• Reinalter, Helmut - Josephinismus als Aufgeklärter Absolutismus (ISBN 978-3205777779)

• Röskau-Rydel, Isabel - Deutsche Geschichte im Osten Europas - Galizien, Bukowina, Moldau (ISBN 978-3886807819)

• Statistische Monatsschrift der k.k. statistischen Central-Commission