It appears that since the city updated the website they do not offer an easy way to download video files. Here's a more roundabout way:
Go to your meeting agenda page for the relevant department. Click on the meeting. At the bottom the video will be posted. Right click on the video and "open frame in new tab".
Here's a new skill for you which requires a little digging into the code - View source for the page - you may need to enable preferences for "Developer Tools" in your browser. Search for "archive-stream". It will give you a string that looks like this
take that <string of numbers> and drop it into this URL:
http://archive-media.granicus.com:443/OnDemand/oakland/oakland_<string of numbers>.mp4
Paste that into your browser and your download will start.
To download video of Oakland City official public meetings:
1. Go to this page: http://oakland.granicus.com/ViewPublisherRSS.php?view_id=2
2. Find the meeting you are interested in and click the Download File link and Save the file.