That would be very hard to implement and extremely abuseable by salty players. How do you know your opponent is not a very slow guy who just needs every second of their turns to play their cards or plan turns ahead? Or how do you know if your opponent is just super busy doing other stuff while playing Hearthstone?
I once received a warning (via email) from Blizzard a long time ago. After playing some games of Heroes of the Storm, I started making stupid dick jokes on chat during a match, but without trying to offend any particular teammates and playing normally. We won (I remember playing with Illidan, who was very OP at that time), but some asshole still reported me. Seems like he or she did not share my sense of humor. :P
It is like these people have no family, friends or whatever and aren't used to innocent jokes like that on a daily basis. But yeah, I know, this is the internet after all.
When someone reports, does Blizzard always punish the reported person or do they investigate further?
Did you send him a death threat in response to his comments? If that is not the case, there is nothing you should worry about, except if you have been just as toxic as him in the past with many other players, of course. In that case and if they decide to investige further, they will probably send you just a warning through an email, but nothing more. All depends on your comment history on Battle.net.