It depends on the video source on but some of the video options on a place like dramanice you can "download" the stream of the video right from the website with developer tools. You don't need to download a plug-in, you don't need to trust someone uploaded the real video.
Look into enabling developer tools (not an extension or an app). It will look slightly different in every browser but they all do the same thing and will have the same options of "Network", "Media".
Here is an example I posted a while ago in the Chrome browser: