RewriteEngine On
RewriteBase /
# Rewrite www.domain.com -> domain.com -- used with SEO Strict URLs plugin
RewriteCond %{HTTP_HOST} .
RewriteCond %{HTTP_HOST} !^themesmodx\.com [NC]
RewriteRule (.*) http://themesmodx.com/$1 [R=301,L]
# The Friendly URLs part
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?q=$1 [L,QSA]
RewriteEngine On
RewriteBase /
# Rewrite www.domain.com -> domain.com -- used with SEO Strict URLs plugin
RewriteCond %{HTTP_HOST} .
RewriteCond %{HTTP_HOST} !^ivory-demo.themesmodx\.com [NC]
RewriteRule (.*) http://ivory-demo.themesmodx.com/$1 [R=301,L]
# The Friendly URLs part
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?q=$1 [L,QSA]
<?php
define('MODX_CORE_PATH', '/home/themesmo/public_html/core/');
define('MODX_CONFIG_KEY', 'config');
?>
/* Initialize the default 'web' context */
$modx->initialize('ivory-demo');
This question has been answered by trussframework. See the first response.

Are you sure the site_start on the ivory-demo context is correct? 21? I would expect home.html, if that's the site_start, to redirect to the root as in MODX the homepage doesn't have a separate url...
I'm not really into Revolution but maybe you need to change this?
define('MODX_CORE_PATH', '/home/themesmo/public_html/ivory-demo/core/');
<html> <head> <title>IVORY | THEMESMODX premium MODX themes & templates - Home</title> <base href="http://ivory-demo.themesmodx.com/" /> </head> <body> </body> </html>
The weird thing here is that when you look at the source code, you get this:
<title>IVORY | THEMESMODX premium MODX themes & templates - Home</title> <base href="http://ivory-demo.themesmodx.com/">
That leads me to believe that something must be funky with a chunk or snippet that you're using. Also, there's no Doctype, although I doubt that would be the cause of this issue.
I know it's a silly question, but are your templates set properly? Are your chunks and/or snippets working as they should? I am asking these questions with the utmost respect, as I know that you're a talented developer, but sometimes an extra pair of eyes can help, and sometimes it's the stupidest mistake that cause these types of errors.