I think Mozilla is marketing this wrong. Triple-AAA titles go for squeezing every last ounce of system performance. I don't think there is anything to be gained to putting a game like Titanfall, which has 5 gigabytes of assets (some UE titles are much bigger and need blu-ray distribution) inside of a browser. Long downloads, long startup, half performance.
But there is enormous value of running casual games with asm.js. Something like Clash of Clans, or Flappy Bird will run just fine. Pitching that asm.js is going to scale games from mobile up through desktop performance I think is overselling things and bound to lead to disappointment.
Rather than believe we're going to get Call of Duty running acceptably on Firefox OS. Let's first settle for CSR Racing, or HayDay.