Does this also map child pages?

To map specific pages you will need to edit the file domain-mapping-system/dms.class.php using the plugin editor and change the code as follows in private function setCurrentDomain()

Find:

$this->domain    = $_SERVER["HTTP_HOST"];

Replace with:

if ($_SERVER["REQUEST_URI"]=='/') {
     $this->domain    = $_SERVER["HTTP_HOST"];
} else {
     $this->domain    = $_SERVER["HTTP_HOST"].$_SERVER["REQUEST_URI"];
}

Also, in the plugin settings, make sure to include a trailing slash “/” after the specific page name in the url. Example: domain.com/page/

The code from Chris Cash works great! It took me a while to find it, author might consider adding this to plugin description

I can confirm that Chris’s code edit above makess mapping sub pages possible.

This would be a great addition to your plugin.
This allows people to make a microsite with more than one page.

Lets say your main site is http://www.widgets.com
You want to make a training website for showing customers how to use your widgets.
For this, you purchased http://www.widgettraining.com

Rather than install a whole new WordPress site or enabling a multisite for this, we could just use your plugin to route the new doamain’s traffic to a specific page on widgets.com

With the default plugin functionality you could map the domain:
http://www.widgettraining.com
to route traffic to
http://www.widgets.com/training

With chris’s edit above, you can map sub pages to expand the microsite like mapping:
http://www.widgettraining.com/widget-a/
to:
http://www.widgets.com/training/widget-a/

With body class CSS and page templates, you can then give the look and feel of an entirely different site on the same installation of WordPress.

Add the following plugin to change the nav menu per page:
http://wordpress.org/plugins/ce-wp-menu-per-page/

As a reminder, you need to add www versions of your mappings to cover all traffic routes.