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.