The WordPress wp_get_shortlink() function has an inherent assumption that, if you pass in no ID or a zero ID, then it checks the current post and uses its ID to determine which post it should return a shortlink for. This is the case in a lot of WordPress "Loop" functions, where zero means "current post". 

Thus, using a bare call to wp_get_shortlink() on, say, the main index template page (or any page where there's more than one post in the Loop) will fail to return the proper shortlink.

The problem lies in this code:
if( !$id ) {
       global $wp_query;
       $id = $wp_query->get_queried_object_id();
}

That's not the right way to get the ID for the current post in the Loop. That will work fine on single post pages only, anything that queries multiple posts will not have it return the proper ID for the current post.

To handle this correctly, the plugin needs to also get the $context parameter from that filter (which it is not currently getting) and then it should implement this code:

    global $wp_query;
    $post_id = 0;
    if ( 'query' == $context && is_single() ) {
        $post_id = $wp_query->get_queried_object_id();
    } elseif ( 'post' == $context ) {
        $post = get_post($id); // note, $id is passed in from the filter arguments
        $post_id = $post->ID;
    }

When the $context is "post", then the user is requesting the shortlink for a specific post. And in that case, it should get the current post ID from the loop, then return a shortlink to that single post page.

When the $context is "query", then the user is requesting the shortlink for the current page, whatever it is. That can be the home index page, or an archives page, or whatever. As you see, this needs special handling for the is_single case, because then you are returning the same shortlink as for the "post" $context.

This will also allow the plugin to be able to generate shortlinks for non-single-post pages, including the home page, BTW. Just check for that "query" $context type.