Broadcasting my computer screen Directly to my TV via LAN

Okay here's a tough one for you folks.

I am considering setting up a Starcraft II tournament at my house. What I would like to do is have two computers in separate rooms for the players and one computer set up as the commentator's desk. The commentator's desk will have Starcraft running and will be spectating the game as well as broadcasting the tournament using Xsplit to twitch TV.

That's the easy bit. The hard bit is that I would ALSO like to broadcast (live) the same video stream to a smart TV I have set up in a different part of the house for an audience to watch the tournament. Since this is in my house I don't have any kind of sound proofing setups so the players will be in their own rooms separated from the commentator and the the audience on the other side of the house which should suffice.

I would like to do this over lan, without needing to use another computer as I don't have one available.

The TV is a 46 inch Samsung 7000 series smart TV with a fully functional web browser. It can watch Twitch TV streams and such so it CAN in theory do the job (Flash player functionality and such). The problem is getting the video over lan to the TV without having to go through twitch as a 3rd party.

Ideally I would be able to type in the local IP address of the commentator's computer in a web browser and the stream will pop up as raw video that can be maximized but I understand that this is probably a naive dream.

SO realistically without needing a laptop to plug into the television can this be done with the resources available to me? I made a post on the Xsplit forums about the delay server and lan functionality of the program but I believe you need to have another computer to view the lan stream using this method (I can't find much information about it and I didn't get a response to my post there)

If I can't use Xsplit that's fine. Broadcasting just the raw screen of the commentator's computer will be enough. It just has to be over lan.

Any ideas would be greatly appreciated. This is the last hurdle I need to overcome to get this going!

Thank you!