That page explains fractional reserve banking in a misleading way.
It's a bit like the famous missing dollar riddle. Taking their example, Alice goes into a bank and deposits $1000 in cash. The result of this is that she no longer has the $1000, and if she is confused on this point a thorough search will prove that she definitely does not have the cash any more. What she does have is a bank balance showing a credit of $1000. This is not $1000. It is a debt owed by the bank to Alice. It is easy to confuse an obligation to pay $1000 with $1000, but they are not the same thing. If you are in any doubt, imagine going into a takeaway pizza place, ordering a pizza, and paying ten pounds. You obviously do not have the ten pounds, but you don';t have the pizza either as it does not yet exist. Instead the pizza place has an obligation to provide you with the pizza. After a short delay, they will (hopefully!) produce the pizza, discharging their obligation. At no time are you likely to be in any doubt whether you have the pizza or the benefit of the obligation. (Uless you are very drunk, I suppose).
When Alice deposits the $1000, she has $0, the bank has $1000 and an obligation to pay $1000. If the bank now lends $900 to Bob, the bank has $100, Bob has $900 and an obligation to pay the bank $900, the bank has an obligation top pay Alice $1000, and Alice has $0. $100 + $900 is still $1000. If Bob deposits the $900, he is left with $0, the bank gets $900 and an obligation to pay Bob $900. So the bank now has $100 + $900 = $1000. If the bank now lends Chloe $810, the bank has $100 + $90 and Chloe has $810. $100 + $90 + $810 = $1000. And so on. At all times the money adds up to $1000. No money is created. What is created is a sequence of obligations for the bank to pay $1000, $900, etc.
It's easy enough to see why people think that an obligation to pay money is the same thing as money because money used to be an obligation to pay. On the gold standard, a pound was an obligation to pay a specific amount of gold. This is why Sterling notes have written on them "I promise to pay the bearer on demand the sum of...".
If you consider an obligation to pay is the same as money, then it's not the fractional reserve bit that creates money, but the banking bit. When Alice deposits $1000, if you consider the bank's obligation to pay her $1000 to be actual money, then Alice has $1000 and the bank has $1000, so the act of making the deposit has created $1000. What the bank does after that is irrelevant (except insofar as it could create evenmore money). In fact, it's not specific to banking. Suppose Alice lends $1000 to Bob in return for Bob writing an IOU for $1000. Since this is an obligation to pay, it's as much money as $1000 in a bank, so Alice has $1000 and Bob has $1000. If Bob lends the $1000 to Chloe, in return for an IOU, Alice has $1000, Bob has $1000, and Chloe has $1000. Chloe can now lend the $1000 to Alice in return for an IOU, leaving Alice with $2000, Bob with $1000, and Chloe with $1000. They have all gained $1000 as a side effect of the debt circle. No banking involved of any kind.