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.