NOT gate with transistor
For the purposes of the NOT gate, you are looking at voltage and not looking at the current. The next "logic unit" that follows will be designed to consider the voltage at OUT, not the current.

Mostly.

In order to consider the voltage, the next circuit will necessarily sink or source a little current (into or out of OUT.) So in reality some current also actually does get exchanged through the OUT pin. And the more logic unit inputs you tie to this output, the larger this current becomes. At some point, the circuit you show won't be able to properly do its job. So there is a limit called "fanout."

But for understanding it, you only need to realize that it is the voltage present at OUT, not the current, which defines the meaning of OUT.