It's because LoL is more popular than Dota in some countries (USA for example). They were first introduced to it, they like it. I was first introduced to Dota, I like Dota. I think it goes somewhere along those lines.
I do think too that Dota players watch less because the picking phase takes forever. It's much more fun to just get in the game client and play it by yourself (I tried to watch today Mouz vs coL, in the picking phase I was like "ahh, I guess I'll play Dota instead or else I'll end up just watching and not playing").
Also, try comparing soccer to basketball: One takes forever for a goal to happen, most of the time it will be even, it's rare for more than 3 goals to happen in one match and etc etc, not only that but it takes 90 minutes to end. That is the argument that some of my friends were using against me and saying that basketball is much better, lots of scores all game, action packed and etc...
But in the end, I enjoy watching soccer, that's what I grew fond of, that's what I love! Maybe this is the same case between LoL and Dota? I reckon that even though soccer and basketball are very different, and LoL and Dota are much less different than the example I mentioned, I still think it might be the same case.
Although I am on Dota's side, I tried LoL before, played with people who are close to me, I still would enjoy Dota more. And personally, everyone that I know that was a former LoL player, they end up saying that Dota 2 is light-years ahead of LoL. Of course, that's personal experience so I can't speak for everybody.
Maybe these streams please them the same way people would (and they do) watch a live chess match? Or is it because Dota players like to watch VODs or replays more than the live thing? I have no idea. Someone should run a research!