Using a rotary switch
If I understand you well, it's very easy.

Assuming the 4 outputs of the switch will be connected to 4 GPIO's you just can check for the state of each GPIO and act on it

// Pin numbers where switch 1 to 4 are attached to.
#define PIN_SWITCH_1  8
#define PIN_SWITCH_2  9
#define PIN_SWITCH_3 10
#define PIN_SWITCH_4 11

unsigned long timer_value = 1000; // No switch selected

void setup()
{
     // Set switch pins to input mode.
     pinMode(PIN_SWITCH_1, INPUT); 
     pinMode(PIN_SWITCH_2, INPUT); 
     pinMode(PIN_SWITCH_3, INPUT); 
     pinMode(PIN_SWITCH_4, INPUT); 

     // Check switches
     if (digitalRead(PIN_SWITCH_1) == HIGH)
     {
         timer_value = 30000;
     }
     else if (digitalRead(PIN_SWITCH_2) == HIGH)
     {
         timer_value = 60000;
     }
     else if (digitalRead(PIN_SWITCH_3) == HIGH)
     {
         timer_value = 90000;
     }
     else if (digitalRead(PIN_SWITCH_4) == HIGH)
     {
         timer_value = 120000;
     }
     else
     {
         // Keep default value
     }
 }

 void loop()
 {
     // Here you can use timer_value to check for the end of the game.
 }