Bitcoin is not a money system as money systems transfer either goods (commodities) or entitlements. Bitcoin, on the other hand, is a system for transferring digital membership certificates. Membership certificates are not money.
You seem to be using a definition of "money" that is different than most.
Most people would agree that:
Money is any item
or verifiable record that is generally accepted as payment for goods and services and repayment of debts, in a particular country or
socio-economic context. The main functions of money are distinguished as: a medium of exchange, a unit of account, a store of value and sometimes, a standard of deferred payment. Any item or
verifiable record that fulfills these functions can be considered as money.
Using this, far more common, understanding of money... Bitcoin is a money system.
...but record of ownership, and not record of membership. Characters on a membership card of a local soccer club are also "verifiable record", but are not money. Of course everyone is free to view them as money and trade their property for them, but that's irrational as they are worthless. P.S. The video is edited so you can check the new version that has more details.