Parties are not an official part of the system, but you can say they're a natural outgrowth of it, specifically of the right to assemble.
As much as people rail against them, I've yet to hear any solutions to the problems they are said to present.
Your quote makes an interesting point.
The good news is that nothing in the Constitution requires a two-party system, and nothing requires the country to hold simple plurality elections
Article I, Section 4, Clause 1: The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Places of chusing Senators.
The problem is we can't get the Congress to agree on whether day is not night, whether money is or isn't speech, whether black people have a right to vote in places like Fulton County in Georgia or Harris County in Texas, whether a multi-national corporate giant is a "person" ... or whether this crap constitutes a denial of people's civil right to vote: