How to Create a single page within a module and set page variables?
The link in my comment may not get you all the way there so I am adding a working example. Assuming everything else in your code is working changing this line

 return array('variables' =&gt; array("var1" =&gt; "Hello World Attempt #2") , '#markup' =&gt; '&lt;p&gt;This is some markup content displayed correctly in the page&lt;/p&gt;');


to

$output = array("var1" =&gt; "Hello World Attempt #2" , '#markup' =&gt; '&lt;p&gt;This is some markup content displayed correctly in the page&lt;/p&gt;');
return theme('page', $output);


Added the entire $output array to the hook_preprocess_page`.

NOTE: You may have to add a theme callback to your menu item. Example here.