The form ID is used as the id attribute on the form when it renders.
For content types the pattern is also predictable: node_[TYPE_NAME]_formnode-[TYPE_NAME]-form. So in your case you're looking for: hook_form_node_videos_formhook_form_node_videos_form_alter().
Another way to handle it is to use the main hook_form_alter() and check the $form_id parameter when you load the form you'd like to target.