I like to watch people play games for a variety of reasons.
One, to learn from them. For instance, I have almost a thousand hours on EU IV. I thought I was pretty decent at it. Then I started watching people like DDRJake (before he went to Paradox), Arumba, and Florryworry and quickly realized how much I could learn from them. In the Civ series, I watched MadDjinn to get better. When I raided hardcore in WoW, I watched the highest end players of my class to see how they reacted to certain situations.
Two, I enjoy their presentation of the game. If I found the host engaging, I'm more likely to watch them. I've cut out most of my TV watching (pretty much only the news and sports are left) and have replaced it with Twitch/Youtube watching. Generally speaking, I'm happier. Although I do have to catch up on Rebels.
Three, and this is specifically about RPGs, I enjoy watching others take part in hobbies that I also enjoy. I like to see what they do and imagine how I would run such a scenario or if there is a NPC or quest item I could steal to make my games better. Most of the time I have these games on at work like a podcast. I've listened to hundreds (probably closer to a thousands) of hours of gameplay. I've learned things that make me a better DM and a better player. I'd say it's worth it.
You don't have to watch and I respect anyone who doesn't or doesn't have the time to watch. But I really like Twitch and recommend it to everyone to at least try and see if it would be something they like.