Writing to you on a tablet, I mention this as I tried last night but I guess it timed out and it never posted. It was way to lengthy to try again...but I've had some sleep and will copy before posting incase it happens again.
There is a way, but at best it is convoluted and very tech heavy. Honestly, you might be better off waiting to see of byutv starts to support Chromecast... I've seen many forums requesting that from them so it might be better to wait and see...but if you absolutely MUST have it..there's only one way I've been able to divine.
You'll need serviio and aVia. Serviio is a free - with option to pay for - dlna server. Everyone should know what aVia is by now. I can not say with 100% certainty, but I'd hazard a guess the video is rtmp which is why vGet doesn't recognize it.. if I'm right you'll need to install a rtmp sniffer..there's about a billion of them, most free, others not. If it's not rtmp then I can't figure why vGet doesn't see it...but you could use something like getflv or something more free...the whole purpose is to get the url the video is pulling from. Armed with that you can head over to serviio and add it to the online media tab.
Confused? Good, cause it gets worse. Chances are this video may not be compatible with Chromecast and if that's the case, you're going to need to get serviio to encode it on the fly...which is simple, however, serviio does not a profile built in for Chromecast. Do a Google search for Serviio Chromecast Profile AllCast, that will get you to the profile you'll need to add. With the profile, you're now going to need to get serviio to "see" the Chromecast. It doesn't do this by default as Chromecast it's not a dlna device. Instead, you'll need to assign a static ip address to something..say your computer. Let serviio cache that ip (it'll stay cached until you remove or upgrade serviio), then manually assign that ip address to your Chromecast. Once done, in the profiles page you need to change the profile of both your android device running aVia and the Chromecast to the AllCast profile I mentioned earlier.
It will work this way, android with tell serviio, via aVia, to play the online media. Serviio with download and encode the media so that's it's compatible with Chromecast, and then serviio with send the media to Chromecast which will then display it.
In this manner ANY online media is technically playable through Chromecast but...the set up and execution takes a flare of mad cap genius and elbow grease.
Not claiming that there might not be an easier way..God knows maybe bubble, playon, plex, etc might be able to do it in a simple straight forward manner.. just saying that this one will work....and not just for byutv, but for anything. Good luck! Personally, . I'd wait hahaha (edited to mention that it did happen)