What the BOJ Actually Controls

What he failed to mention was the fact that BOJ doesn't control the money supply, it controls the monetary base (cash and BOJ reserve accounts held by depository institutions, i.e., banks). Denote the monetary base by MB.
The BOJ influences the money supply by controlling MB and allowing fractional reserve banking. The reserve is the amount of money banks must keep on hand in "cash", nominally to serve depositor demands for their money.
In fact, the reserve is not cash (currency and coins). Nor is it needed to supply depositors demand for payments (it's much bigger than that). It is a regulatory tool.