How can I include the user id inside of a shortcode php output?

So I’m assuming the “current commenter” is actually the current user logged into WP. So to get the current user ID, you can simply use get_current_user_id:

echo do_shortcode("[theplugin_user_data user_id='" . get_current_user_id() . "']");

UPDATE

Ok, so we want, then, the comment’s author ID:

//$comment = get_comment(); // in your case, it seems you already have a $comment object...
if($comment) {
    if($comment->user_id) echo do_shortcode("[theplugin_user_data user_id='" . $comment->user_id . "']");
    else echo '(no data available)'; // <---- fallback, in case the comment has no known author
}

Hope this helps!