To set a button that makes such action, you have to access the Mighty Button Properties panel and go to the Action submenu. Once there, choose the option External link on the drop-down parameter Action. When you mark this selection, a new field will show up right below, the URL field. Type or paste the website URL you would like to load after interacting with the button.
The URL you have set will open in a new window or tab of the browser and video playback will automatically pause.