How to create tension in old upright handle bar levers / U brakes?
Well done for adding the video link - I saw the problem immediately.

The problem is in a brake lever. The body of the lever must hold the outer housing and pull the cable through it. Your housing goes through the lever body and touches the lever, and is pulled by the lever along with the cable. 

You are missing the barrel adjuster mechanism on the lever that the housing fits in to but cannot pass through (it has a smaller hole for the cable).