Your overall argument may not be wrong, but your interpretation of maps and dismissal of the cartogram is dead wrong. This is the most basic and classic misinterpretation of a map. Did Trump win more counties? Yes. Did he win more votes nationwide? No. Did he win more votes in the key states that gave him an electoral college advantage? Yes.
The area taken up by a county that is large and sparsely populated is a misleading visual. Counties are essentially arbitrary shapes and sizes, people are are still people — 1 person, 1 vote. The cartogram is providing a visual representation of people instead of arbitrary political borders, which have no actual bearing on the election.
If our elections were decided by the highest total combined area of the counties with a majority vote total for that candidate, the counties map would be useful. Donald Trump won the election legitimately, through the electoral college. No need to use bad map interpretations.