Current ALWAYS flows in a circuit.
In this simple example the current flows from the
Power Supply -> Pi -> GPIO pin -> LED -> resistor -> Ground (and thus back to the Power Supply).
In a series circuit it makes no difference which order the components are connected (although with polarised components, such as the LED, they need to be connected the right way round).
I should point out that while the article you linked is a good beginners description, it contains a number of factual errors, in particular the resistor colour code.
From an purist engineering point of view the best connection would be
+3.3V -> resistor -> LED -> GPIO pin (just to be clear the GPIO pin then needs to be LOW to light the LED).