I found an answer to my own question. The solution is a wee bit of an inconvenience, but certainly not much more effort.
SOLUTION: Open VLC, then "Toolbar - Media - Open File". In that 'Open File' dialog, browse to the LAN location where the video is located, and open it. The file can be on a mapped drive, or not -- in which case, just browse Network until the file is found.
As soon as I discovered that, it was an 'ah-ah' moment. Years ago, while using MusicMatch Program, a similar Windows File Explorer error occurred. I could not access music via the "new and better" Windows 8 File Explorer. The solution there was to put the complete path into the playlists, instead of just a shortened path without a Drive:.
So it seems that with (at least) Windows 8 and above, the arguments passed from Windows Explorer to an application -- when double-clicking an object -- have changed. The older applications do not understand the new format, and therefore, cannot open the object properly. Leastwise that is my non-programmers reasoning.
In any event, I hope my little conversation can help others with similar problems. Chow.
What happens if you copy the file from the cloud storage to your machine's drive and open it with VLC there? – mvw – 2018-01-17T08:26:19.720