Menu items in Joomla server several different purposes other than providing links for users to get to content. If you are using the core SEF URLs, this is the first place Joomla looks to create those URLs. In general a URL is built like this - joomla install/parent menu item alias/sub menu item alias/content item/article alias.html. Since your video category does not have a corresponding menu item to use for building URLs, it uses the default URL scheme.
The menu item is also the source for the itemID that every page uses. If a particular page does not have a related menu item, it will inherit the itemID from the previous page usually or in the case of k2 items/joomla article it will inherit the itemID from the menu item that links to the parent category of the content. The itemID is used to determine module menu assignment. This is why getting to a particular page that does not have a menu item 2 different ways will often give you pages that look different, different itemIDs were inherited resulting in different modules being displayed.
Since Joomla really counts on the itemID, you should always specify a menu item for any content you are diplaying, even if you do not want to display a link in the menu. By creating a menu that does not appear in a module, you still get the itemID you need for the content, but the menu never appears anywhere. Usually, a link to a category will be enough since child content will pick up that itemID, but in some cases it makes sense to create menu items to specific content items/articles. You would do this any time you want a specific URL for an item. For example, if you wanted to create a URL like your-site.com/special-offer, you could create the content item for the special offer, then make a menu item with the alias special-offer to get the correct URL.
Joomla also uses the menu item for browser titles and page titles. Your question is not related to that so I'll stop here, but as you can tell it is pretty important to know when to create a menu item for your