On macOS, launchd is used to start the webservice. An example configuration file can be found in $HOME/Library/LaunchAgents/org.virtualbox.vboxwebsrv.plist. It can be enabled by changing the Disabled key from true to false. To manually start the service use the following command:

launchctl load ~/Library/LaunchAgents/org.virtualbox.vboxwebsrv.plist

For additional information on how launchd services could be configured see:

https://developer.apple.com/library/mac/documentation/MacOSX/Conceptual/BPSystemStartup/Chapters/CreatingLaunchdJobs.html.