Do I need video controls for looping background videos?

Yes, if information presented in parallel with other content starts moving automatically and moves for more than five seconds, controls must be provided for a user to pause, stop, or hide the movement (unless essential to the activity, but that does not seem to be the case for a video being used as a background image). This is defined in the WCAG 2.0 Level A success criterion 2.2.2: Pause, Stop, Hide. One motivating factor behind this rule is that moving content can be distracting for some people.