You sould finish that original quote by saying that this "is next to impossible." I believe the writer was responding to an earlier criticism of the popular vote system by replying that this would be very rare, as rare as the Electoral college system's extreme example. Both systems have scenarios in which Presidents are elected in bizarre ways.

You said, "Imagine that every four years our president gets elected exclusively by 20 states or less." But, government is for the people, not for "imaginary beings called states" (James Wilson, Constitutional Convention). James Madison, the Father of the Constitution, wrote "…the President is to act for the people not for States." Under the Electoral College, this isn't the case; instead, every vote is not equal, and the President doesn't represent the people. What you call "mob rule" is merely majority rule, and I agree, the majority should rule.