I refer you to the wiring schematic of a push button connected to the Arduino (you may ignore the external LED):
Here's what happens when the button is pressed:
The 5V voltage signal from the 5V pin (point 1) will propagate (travel) to the pin 2 input (point 2).
Pin 2 is an input, which means that it has a very high internal resistance (impedance). As a result, there will be very little current flowing. There fore, there is no short circuit. A short circuit is one in which very high current flows.
Noticed the pull-down resistor at point 3, between the button and the GND pin. Some current will flow through this resistor. However, because the value of this the resistor is reasonably high (usually at least 10 kΩ), again, not much current will go through it, and that is also not a short circuit.