Shortcode is not processed when added to option field using wp_editor

WordPress applies various filters to the content before it is output. The filter do_shortcode is the one that processes shortcodes. You can apply all of the same filters to the output of your editor by using the following code:

echo apply_filters( 'the_content', get_option( 'piedino_plugin_var_testo' ) );

Here is the list of all of the filters applied to the_content:

add_filter( 'the_content', 'capital_P_dangit', 11 );
add_filter( 'the_content', 'wptexturize'                       );
add_filter( 'the_content', 'convert_smilies',               20 );
add_filter( 'the_content', 'wpautop'                           );
add_filter( 'the_content', 'shortcode_unautop'                 );
add_filter( 'the_content', 'prepend_attachment'                );
add_filter( 'the_content', 'wp_make_content_images_responsive' );
add_filter( 'the_content', 'do_shortcode', 11 ); // AFTER wpautop()