You code seems to be correct. Try the following instead.
$args = array(
'labels' => $labels,
'public' => true,
'publicly_queryable' => true,
'show_ui' => true,
'query_var' => true,
'rewrite' => true,
'hierarchical' => false,
'menu_position' => null,
'supports' => array('title'),
'capability_type' => 'video'
);
Update:
You have to do some extra steps before making it work with the members plugin. See this forum post from Justin Tadlock (developer of the members plugin).
http://wordpress.org/support/topic/anyone-managed-to-get-custom-post-types-capabilities-working/page/2#post-1593534
This plugin seems to be doing it automatically:
http://wordpress.org/extend/plugins/map-cap/