Do the I/O pins on Arduino read current or voltage?
They read voltage.  When you close the pushbutton switch the input should have a 0V or digital &quot;0&quot; on it.  When you open the pushbutton the resistor should pull the input to 5V or digital &quot;1&quot;.
Yes, it is still connected to +5V via the resistor but the nearly 0 Ohm switch pulls the line all the way (or very close) to 0V.