How to translate get_intermediate_image_sizes?

You can use __(), _e(), _x() or _ex() and your textdomain to make your theme or plugin translatable.

I stripped your code snippet to the basics, so you will get the idea more easily:

<select class="widefat">
  <?php foreach ( $this->getImageSizes() as $name => $atts ) : ?>
    <option value="<?php echo $name; ?>" ?>>
      <?php echo ucwords( __( $name, 'textdomain' ) ); ?>
    </option>
  <?php endforeach; ?>
</select>

Unfortunately internationalization is not possible with variables like $name so you will have to provide the default image size names to make them accessible:

$sizes = array(
  __( 'thumbnail', 'textdomain' ),
  __( 'medium', 'textdomain' ),
  __( 'large', 'textdomain' )
);

If you’re adding the image sizes yourself you can avoid the hack above if adding them like this:

add_image_size( __( 'custom-image-size', 'textdomain' ), $width, $height, $crop );