I have a recent version of Windows 10.
Yes, inside of a browser you can Chrome cast to a TV set that accepts the HDMI interface of the Google Chromoplast stick.

But know how to do that.
I want to do it without the browser. I have at least one application that does  video and I can not find the URL for the video.
The workaround is to download the video and play it in a browser. But I would like to just do it without needed to download it.
Any ideas? I have read the articles from Google and I must be missing some kind of detail. They say you can cast the whole screen to the TV. I am stuck. I don't get it.
Thanks.This is one of the many reasons why my chromecast was tossed into a box with other junk.  Chromecast wants to run through Chrome or no cigar. To get full screen does F11 work or does that only work for PC SCREENS. I gave up on my chromecast YEARS ago very SHORTLY after wasting money on it.

I was going to sell my chromecast to TRY to get $20 of my $35 back and its associated with my gmail account and permanently bonded to my e-mail. In order to sell it i would also be required to give them my e-mail account, so its a piece of junk to me. Maybe someday it will be worth something 30 years from now to a collector as its in the box with other junk, doesnt take up much space, and I might get something of that $35 back. 

For some people the chromecast might work out perfect for them, but not for my home and our needs. I have a Roku model 1 as well as my BluRay player has ability to attach a up to 32GB external drive to it to play movies in FAT32 so i found a purpose for an old 40GB IDE Laptop drive formatted with a 32GB partition with a USB/IDE adapter, as well as I can Plex to these devices if I wanted to using a system as a media server.Thanks for sharing.
The TV set in our dining room has HDMI and the AV type connectors.
I am able to use the chrome cast to send the browser content from my desktop to the dining room. So far I have not been able to do it without the  using Chrome browser.

However, I can push the browser over to my second monitor and the TV still shows only the browser content. In that case somebody can see a video in the dining room while I do something on my computer with the main monitor.

Like you said, Roku does not have this limitation. I use a Roku in the bedroom. So far I have not found out how to use Roku with a local media server. I was hoping the Chromecast would do the job.   
Roku supports Plex Tv .... https://www.plex.tv/

https://www.plex.tv/how-it-works/

I have been using my Sony BluRay player that has ability to play local movie files through a FAT32 (40GB laptop hard drive formatted to 32GB) through its rear USB port. But I did play with Plex and while the free version works the premium has more features.The Chromecast chrome extension ALREADY allows you to cast your entire screen, when it opens, click "Cast To" at the top which will open a menu that lets you select "Cast Tab" or "Cast Desktop" - Simply select "Cast Desktop" and it will share your entire screen.