I see no reason why what you pictured wouldn't work. As always, make sure your speakers have at least 4 ohms of resistance.. but most home audio stuff is 6 to 8 or more.
I'm not sure how much that amp costs or what you are trying to do, but I would at least consider investing in a 5.1 A/V receiver of some sort. They will offer more flexibility and potential for surround sound, a subwoofer, eq settings.. like I said, they can just do more.
But if all you want to do is make your tv louder, I would say that will work fine.
i received my amp today, but having trouble setting it up. when i connect it directly to my sky box it works fine through the amp then speakers, but when connect to the RCAs on the TV there is nothing, and there is no analogue on my xbox one which everything runs through anyway.
help would be much appreciated on how i can get this working.