Jaksta Media Recorder is well known as an all in one Dropbox Downloader, Dropbox Recorder and Dropbox Capture Tool and allows the downloading, recording and capturing of Video, Music and Radio.
Its easy to use Jaksta Media Recorder to record from Dropbox. Simply play Dropbox in your browser, and a copy of the Dropbox video is downloaded to your PC. You can also just drag and drop (or cut and paste) webpage urls containing videos directly from your browser and Jaksta Media Recorder will extact the video. Its as simple as that!
More detailed steps are available in the How to Download from Dropbox Guide