I would like to know if there is a way to show posts created by CURRENT user ? I would like to create a personal area for each user and there should be showing table with ONLY their posts.
Im using Serialized PHP array source type and I wrote a WP Query for it screenshot
Is this can be achieved with free version or some other addons required? Or its not possible at all?

Well its really funny that developers didn't posted "wpdatatables_filter_php_array" filter in documentation list. 

I solved my problem by investigating code which costed me a couple of hours of debugging. So to finish this task I added author id as a separate column inside WP Query

$query_args = array(
    'post_type' => 'agreements',
    'posts_per_page' => '-1',
    'post_status' => 'publish',
);

$return_array = array();
// The Query

$the_query = new WP_Query( $query_args );

// The Loop
if ( $the_query->have_posts() ) {
    while ( $the_query->have_posts() ) {
        $the_query->the_post();
        $author_id = get_post_field ('post_author', get_the_id());
        $return_array[] = array(
            'Agreement Execution #' => get_the_id(),
            'Concierge ID' => $author_id,
        );
    }
    /* Restore original Post Data */
    wp_reset_postdata();
} else {
    // no posts found
}
echo serialize ($return_array);

Solution:

add_filter('wpdatatables_filter_php_array', 'show_rows_with_specific_id');
function show_rows_with_specific_id( $PHPArray ) {
    foreach($PHPArray as $key => $value){
        if($value['Concierge ID'] != get_current_user_id()){
            unset($PHPArray[$key]);
        }
    }
    return $PHPArray;
}


For those who's looking for backend filtering I think that's the great option if you don't need to buy premium.