Is there a possibility for major titles becoming "asm.js ports"? Games like World of Warcraft, League of Legends, Battlefield series, Starcraft 2, Minecraft, etc.
Given that asm.js games tend to run at something like 15-30% of the speed of native code, I doubt we'll see Battlefield 4 or Starcraft 2 anytime soon. Additionally, given that the WoW game client is many gigabytes in size, I doubt we'll see that either, even if it could run.
So: Minecraft, yes. The rest? No.