What it says essentially is "the person with the most votes becomes president", via the Electoral College, and that's the entire structure of the process.

So there's always one person with the most votes, and the next person with almost-the-most-votes. Over time that solidifies into two parties.

Under the U.S. Constitution, the president and vice president are chosen by electors, under a constitutional grant of authority delegated to the legislatures of the several states. The Constitution reserves the choice of the precise manner for selecting electors to the will of the state legislatures. It does not define or delimit what process a state legislature may use to create its state college of electors. In practice, the state legislatures have generally chosen to select electors through an indirect popular vote, since the 1820s. Most states use a "winner-take-all" system in which all the state's electors are awarded to the candidate gaining the most popular votes.[5] Maine and Nebraska allow individual congressional districts to each elect one elector.

We first have to get rid of the Electoral College before we can do anything else and that involves removing parts of Article II. Until then, third parties will not get any (or very few) Electors = it's a duopoly.