I know lots of you guys who don't follow Dota will not get it so let me give you the explanation already, copied from a reddit post, with my personal take on at the end.
ESL one has hosted Dota 2 tournaments for a long time, and usually have been pretty great. However, this time they signed a deal with Facebook so that they will only stream their platform. This is a huge change since most people are used to watching Dota games on Twitch or even Youtube to some extent.
To give an alternative to the official Facebook stream, several people started unofficial streams on Twitch, streaming the games using the Dota 2 game client. This basically happens during every large event, and Valve has specifically stated that as long as there are no overlays showing sponsors, etc. it is okay. However, because ESL is streaming on Facebook this time, many people who prefer to watch on Twitch now watch these streams instead of the official stream.
ESL got angry and claimed that these streams are competing with their official stream. and started issuing or threatening to issue DMCA takedowns to these streamers, such as BananaSlamJamma (BSJ) and AdmiralBulldog (Bulldog), to stop them from streaming. As many people and this blog have pointed out, this is an illegal use of DMCA since ESL does not own any of the content related to Dota TV (The way to watch Dota games within the game client).
/r/Dota2 became quite frustrated in part due to the DMCA bans and also due to ESL's unprofessional attitude on twitter. The community produced such a response that Valve now has come in and make an official statement. This statement solidifies the fact that ESL wrongly issued DMCA takedowns.
I believe ESL knew it was in the wrong, or in a very gray area at best but more important they didn't expect Valve to bother and anyone to be brave enough to contest their DMCA. Oh, how little they knew...
On Valve side, I don't think they went out of their way just to protect some streamers, what I believe they are doing is sending a very clear message of who owns DotaTV content. If they didn't act like that it could be harder in the future for them to contest this kind of thing.
Fun fact, Blizzard has legal problems on Korea about broadcast licensing fees of the original Starcraft and this kinda of legal conundrum is what I think Valve is trying to prevent here.
