After accounting for the curvature of the Earth, the distance between (53.92085665, 14.2861684) and (49.0080789, 22.88022362) is 806 km, and the line is very different from what's shown in the article.
I am just guessing, but perhaps your intuition is that the shortest path should lie along a line of latitude. An easy-to-see counterexample would be two points close to the north pole, but with 180 degrees of longitude separating them. In this case the shortest path actually goes through the north pole, rather than around it.
You can also generalize this say that within the northern hemisphere, the shortest path between two points will curve (when viewed on a flat map) towards the north pole.
The first approach (which is a simplification) uses the usual way to calculate a distance between two points on a FLAT plane, which using is the Pythagorean Theorem. So d = √((y1 - y2)^2 + (x1 - x2)^2).
The second approach uses the haversine formula: https://en.wikipedia.org/wiki/Haversine_formula which takes the curvature of the Earth into account, and also the fact that one degree in longitude is a different distance depending on the latitude.