Retrieving plugin options value saved through setting

You are saving data to an option named my_option_name so your attempt to retrieve data from an option named $this->options['title'] isn’t going to work. You will need something like this:

public function DataToget($field = '') {   
  if (empty($field)) return;
  $jugHigh = get_option( 'my_option_name' );
  if (!isset($jugHigh[$field])) return;
  return $jugHigh[$field];
}

With a shortcode like:

if ( !function_exists("getdat_func") ){ 
  function getdat_func() {
    $getdatClass = new MySettingsPage();
    $output=$getdatClass->DataToget('title');
    $output= apply_filters( 'getdat_func', $output );       
    return $output; 
  }
}
add_shortcode( 'getdat', 'getdat_func' );

But really, just roll the shortcode callback into your class:

function getdat_func() {
  $output = $this->DataToget('title');
  $output= apply_filters( 'getdat_func', $output );       
  return $output; 
}

And add this line to your constructor:

add_shortcode( 'getdat', array($this,'getdat_func') );