You need the DVD Player to play the Video_TS files. Launch DVD Player and use the
Navigate to the WD server and select the folder containing the iDVD project you want to open:
and see if that won't play for you.
Each iDVD project's Video and Audio folders should be in their own separate folder.
The above works when those fodlers are on an external HD but I have no experience on a cloud drive so you'll have to give it a try and see for yourself.
My reply has nothing to do with iPads or iPhones as they weren't mentioned in your original post. My answer refers to accessing the Video_TS folder from your Mac with DVD Player.
The Video and Audio folders I used were taken from a disk image of one of my iDVD projects. They would be identical to what one would find on a burned disk.
I copied the Video and Audio folder from another burned disc of mine and tried the same test and it worked. Try it from your Mac. If you have an external HD put the Video folder on it and see if DVD Player can play it.
It's very possible that the cloud server has a different permission setup that prevents DVD Player form playing the Video_TS files. They certainly work on an external HD formatted OS X Extended (journaled)
Sorry Old Toad that you were able to infer all that a Cloud server should be able to offer, but it seems obvious to me that rather than being limited to DVD and Laptop, any Apple consumer would like to access their iDVD content from the internet, including my iPad and iPhone, as the original question does request. This problem has nothing to do with the permissions of the server, but it might be with how the DVD is copied. I may need to make an "image file" type copy. But, somehow, from what I've read elsewhere, and from what I've tried so far, this still remains an unanswered question.