Update 2015-09-19. The number of posts I have done on the subject of Elisa Viihde, Chrome, and VLC has grown, and it was becoming a hassle to update the old posts to link to the newest information, so I decided to create a separate page that will always hold the newest version of my extension and up-to-date installation instructions.
Apparently the way recordings are served out from Elisa’s servers has changed a bit, which caused the “Download” functionality in my Chrome extension to stop working. Thanks to Petri for reporting the problem.
There is now a new version (3.1) of the extension that once again enables you to download a recording.
The installation instructions are like in the old version. Unzip the file, go to Chrome extensions, make sure that the Developer mode box is checked, and choose Load unpacked extension. Detailed instructions in the old post here.
Make sure that you remove (or disable) the old version of the plugin from the extensions list, otherwise you will end up with duplicate links on your page.