When is a resistor actually short circuited?
If its two terminals are connected to the same node, the resistor is short-circuited.

In practical circuits, we might also say a resistor is short-circuited if a much lower value resistor is connected in parallel with it. In this case, the same potential will be across the two resistors, but the lower-value one will carry much more current than the higher value one. 


  In [the first example], current flows through both 8k and 3k ohm resistors. Why is the current not bypassing them completely?


Because of Ohm's law. If there's a potential difference across the resistor, a current will flow through it. 

In this case, the two terminals of these resistors are connected to different nodes, so there is (very likely) a potential difference across them, and thus a current will flow through them.