Keep in mind that the formula for "gross income" from city connections does not subtract the costs of road and railroad segments or harbors (however the city connection is formed). In practice, as the War Academy article states, you do need to subtract those costs to confirm that the city connection is profitable (i.e., generates positive "net income"), but those costs are not formally included in the in-game formula. This is important, because the Macchu Picchu bonus applies to gross income from the city connection, not net income.
So, on the screen, Sparta shows as having city connection income of 10.08, which does not reflect the cost of 6 road segments, which appears "below the line" in the cost of roads and railroads (a total of 16 in the screenshot). So the baseline "gross income" yield from the Sparta city connection is 8.05 -- that, plus 25% for Macchu Picchu, gets you to (more or less) 10.08. I haven't double checked the computation for the other two cities, but this looks fine to me.