I have not seen the video, but the Fed is certainly a monopoly. Money evolved on the free market, and is a commodity. Many commodities were used as money, and precious metals emerged on the market as the best functioning money. Gold and silver are money, according to the market. Paper notes only became traded as money because they were redeemable in gold or silver. There is essentially no demand on the market for little slips of paper, while there is tremendous demand for gold and silver. The production of money was a private, competitive enterprise. Names like "dollar" and "pound" were nothing more than a name for a specific weight of gold or silver.
So called fractional reserve banking is the fraudulent practice of printing up additional paper money that is not backed by gold or silver.
Governments, in partnership with the large commercial banks, forcibly took over and monopolized the production of money. In the U.S., this occurred in 1913 when the Fed was created, and refusing to accept Fed notes in payment of debt was made a felony. Money was still redeemable in gold.
The conspiracy continued in 1933, when FDR's gang confiscated all of the monetary gold from U.S. citizens, and made its possession a felony also.
Large banks and foreign governments could still redeem in gold.
In 1971, Nixon "closed the gold window", meaning not even banks and governments could redeem dollars for gold.
Today, the U.S. government in partnership with the Fed, simply print money to their hearts content, spending and lending it as they wish. In olden days, this was known as "counterfeiting", and was a crime, because it is an effective way to steal real wealth away from innocent people. Now, it is known as "monetary policy".