How does a NAND gate work? (Very basic question)
The boolean equivalent of a 1 is that current is flowing through a point.


That's the fundamental confusion leading to difficulty in understanding the circuit.

Single ended logic like this encodes state as voltage not current.

Inputs of logic gates are designed to source or sink very little current, so the output of the previous stage is easily able to impose its intended voltage on the connection between output and the following input with very little current needing to flow.

Current-mode signaling does exist, but it's generally used only in noisy situations, for example the time-tested 4-20 mA current loop standard.