Server version: Apache/2.2.22 (Debian)
nginx version: nginx/1.6.2

<?php
// путь до сервера mysite.com:8585/controllers/socketserver.php


$socket = stream_socket_server("ws://mysite.com:8585", $errno, $errstr);

if (!$socket) {
    die("$errstr ($errno)\n");
}

while ($connect = stream_socket_accept($socket, -1)) {
    fwrite($connect, "HTTP/1.1 200 OK\r\nContent-Type: text/html\r\nConnection: close\r\n\r\nПривет");
    fclose($connect);
}

fclose($socket);

window.onload = function(){

    var label   = document.getElementById('status');
    //решил, что уж по абсолютному пути достучится
    var wsUri = "ws://mysite.com:8585/controllers/chat-server.php";
    var output;
    if(window.WebSocket){
        var websocket = new WebSocket(wsUri);
        label.innerHTML = '<p class="seedmed">соединение установлено</p>';
        console.log(websocket);
    }

    websocket.onmessage = function(e) {
        alert(e.data);
    };   

WebSocket connection to 'ws://mysite.com:8585/controllers/chat-server.php' failed: Error in connection establishment: net::ERR_CONNECTION_REFUSED