Drupal - How to limit direct access to URLs of nodes that are shown in a video gallery created with Views?

Try content access module and prevent access to video content individually( or also you can set access to it for you desire roles )

This module allows you to manage permissions for content types by role and author. It allows you to specifiy custom view, edit and delete permissions for each content type. Optionally you can enable per content access settings, so you can customize the access for each content node.

Also you can use Node View Permissions module, but I suggest use Content access module.

(if you want work with drupal for future is better getting involve with this useful modules)

Install Node View Permissions module.

Node view permissions module enables permissions "View own content" and "View any content" for each content type on permissions page as it was on Drupal 6.

Now goto permission page and remove View any content permission from video content type for Anonymous user.

In case you want only few of the videos from Video gallery to be accessible to the anonymous user, then install Deny Access module.