Well, I was just wondering… Is it possible for me to stream games on my personal website?
And, if yes, how?

you can stream your games on our public servers, using your own organisation (you may register those for free too) and you can embed a small box on your website listing only your organisations games.

you can see an example of that feature on any organisations profile page on this website. For example the ZOTAC cup organisation: http://www.waaaghtv.com/en/user/orga/ZOTAC/ The left half of that page is that organisations game list, and the embed html code is already printed in the lower right ;)