I've checked the specification of that product which has three different output connectors:
- 1x USB 2.0 Mini-AB
- 1x A/V Mini Terminal (4-pole mini-jack) Outputs
- 1x HDMI C (Mini)
USB 2.0 Mini-AB Probably this won't help you because usually it is for transferring data such as video files, not a live video stream. It is true that there have been a few camcoder models which support direct streaming by being recognised as a webcam, but I couldn't find any evidence that this is one of those.
A/V Mini Terminal (4-pole mini-jack) This can be your cheapest option to get the stream. With the bundled cable, you'll get the RCA-type traditional composite video output and audio output. The video quality may look ugly (Composite video means "SD, interlaced, blurry"), but you don't have to buy something expensive to get live stream. Just a cheap TV tuner card which has A/V inputs is enough. And this must be still much superior than usual web cams in the video quality.
HDMI C (Mini) This is the best option you can take, if you can afford the money to buy a good HDMI capture board. e.g. http://www.ebay.com/bhp/hdmi-capture-card As compressing full-HD stream (on-the-fly) is still a big deal for modern PC, especially if you want more complex codecs which supports higher compression ratio without sacrificing the video quality, you need to check more expensive ones to reduce the workload of your computer during streaming as they support hardware encoding on the board. Probably the cheaper ones make your PC more busy to compress the stream by itself. In addition, don't forget to check compatibility with Twitch TV before buying one. It is because the 'compressed' stream is transferred via Windows filters which become picky sometimes to use with an application. It seems that some products support Twitch TV directly, which will be ideal for you.
Reading this article (from Twitch TV) may help you. http://help.twitch.tv/customer/portal/articles/792769-how-to-broadcast-console-games This is for gaming consoles, but basically what you're going to do is almost the same as that, if you want Full HD streaming.
To sum up, I think it depends on what you want to do in Twitch TV. If you want a cool full-HD live streaming, you'll need to spend more money. If SD streaming is enough for you, go for the cheaper option.