void loop() {
  static uint16_t last_millis;
  static stepperstates xStepState;
  if (PS3.getButtonClick(START)){
    xStepState = RUNTO1;
    StepperControl.moveTo(POS1); // go to POS1
    Serial.print("\n Starting Movement between POS1 and POS2");
  }
  if (PS3.getButtonClick(CROSS)) {
    xStepState = STOPPED;
  }

  StepperControl.run();

  switch (xStepState) {
    case STOPPED:
      StepperControl.stop();
      break;
    case RUNTO1:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT1;
        last_millis = millis();
      }
      break;
    case WAIT1:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO2;
        StepperControl.moveTo(POS2);
      }
      break;
    case RUNTO2:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT2;
        last_millis = millis();
      }
      break;
    case WAIT2:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO1;
        StepperControl.moveTo(POS1);
      }
      break;
  }
}

#define POS1 80
#define POS2 0

const uint16_t DELAY = 200;
enum stepperstates {STOPPED, RUNTO1, WAIT1, RUNTO2, WAIT2};

[...]

void loop() {
  static uint16_t last_millis;
  static stepperstates xStepState;
  if (PS3.getButtonClick(START)){
    xStepState = RUNTO1;
    StepperControl.moveTo(POS1); // go to POS1
    Serial.print("\n Starting Movement between POS1 and POS2");
  }
  if (PS3.getButtonClick(CROSS)) {
    xStepState = STOPPED;
  }

  StepperControl.run();

  switch (xStepState) {
    case STOPPED:
      StepperControl.stop();
      break;
    case RUNTO1:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT1;
        last_millis = millis();
      }
      break;
    case WAIT1:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO2;
        StepperControl.moveTo(POS2);
      }
      break;
    case RUNTO2:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT2;
        last_millis = millis();
      }
      break;
    case WAIT2:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO1;
        StepperControl.moveTo(POS1);
      }
      break;
  }
}

Instead, you probably want to avoid blocking functions and set up a finite state machine and use the run() function of AccelStepper, which you should call as often as you can and it will move the stepper if it's not yet at the target position.

void loop() {
  static uint16_t last_millis;
  static stepperstates xStepState;
  if (PS3.getButtonClick(START)){ // START to start movement between two POS's.
    xStepState = RUNTO1;
    StepperControl.moveTo(POS1); // go to POS1
    Serial.print("\n Starting Movement between POS1 and POS2");
  }
  if (PS3.getButtonClick(CROSS)) {
    xStepState = STOPPED;
  }

  StepperControl.run();

  switch (xStepState) {
    case STOPPED:
      StepperControl.stop();
      break;
    case RUNTO1:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT1;
        last_millis = millis();
      }
      break;
    case WAIT1:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO2;
        StepperControl.moveTo(POS2);
      }
      break;
    case RUNTO2:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT2;
        last_millis = millis();
      }
      break;
    case WAIT2:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO1;
        StepperControl.moveTo(POS1);
      }
      break;
  }
}

Instead, you probably want to avoid blocking functions and set up a finite state machine and use the run() function of AccelStepper, which you should call as often as you can and it will move the stepper one step toward the target position, if it's not yet at the target position.

In the example, there are 5 states, corresponding to all possible combinations of what your program could be doing:

• STOPPED: the initial state, the stepper has no target
• RUNTO1: the stepper is moving toward POS1, but hasn't reached it yet
• WAIT1: the stepper has reached POS1 and is now waiting for a specified delay before moving to the next state. This state uses the process shown in the BlinkWithoutDelay standard Arduino example sketch for delaying without blocking.
• RUNTO2: the stepper is moving toward POS2, but hasn't reached it yet
• WAIT2: the stepper has reached POS2 and is now waiting for the next state

You can also see the situations where a state is changed:

• When START is pressed, set a new target position and enter the RUNTO1 state

• When CROSS is pressed, stop all stepper action and enter the STOPPED state

• When in RUNTO1 or RUNTO2, and the distanceToGo() is zero, enter to the corresponding WAITn state

• When in the WAITn state and the specified time has elapsed, enter the corresponding next RUNTOn state.

Example:

void loop() {
  static uint16_t last_millis;
  static stepperstates xStepState;
  if (PS3.getButtonClick(START)){
    xStepState = RUNTO1;
    StepperControl.moveTo(POS1); // go to POS1
    Serial.print("\n Starting Movement between POS1 and POS2");
  }
  if (PS3.getButtonClick(CROSS)) {
    xStepState = STOPPED;
  }

  StepperControl.run();

  switch (xStepState) {
    case STOPPED:
      StepperControl.stop();
      break;
    case RUNTO1:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT1;
        last_millis = millis();
      }
      break;
    case WAIT1:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO2;
        StepperControl.moveTo(POS2);
      }
      break;
    case RUNTO2:
      if (StepperControl.distanceToGo()==0) {
        xStepState = WAIT2;
        last_millis = millis();
      }
      break;
    case WAIT2:
      if (millis() - last_millis >= DELAY) {
        xStepState = RUNTO1;
        StepperControl.moveTo(POS1);
      }
      break;
  }
}