Correct, in addition, the reason the compiler doesnt throw an error if you put a function WITH BRACKETS there,
is because the on_key function is a VOID*, and if you put a function there
WITH BRACKETS, the compiler assumes you mean to put the RETURN VALUE of the function there.

So if you execute your code with it like that, the function will execute as soon as the
on_key command is reached, regardless if the key is pressed or not, then never again....

[FOOTNOTE] That is also how any EVENT pointer works. Be they PANEL, MATERIAL, ENTITY, or PARTICLE events.