Keep in mind that WebAssembly is still in a super early form. In fact, it's not even in Chrome Beta or Developer channels, it's in Chrome Canary which is the most beta form of Chrome. So if you are looking to take advantage of WebAssembly and check it out, you'll need to install Chrome Canary. But remember that Canary is very early beta, or even alpha, so you'll likely find loads of different bugs and other issues with Chrome in this version. However using it and testing it out can help Google get feedback on what needs to be fixed to make WebAssembly and even Chrome in general, easier to use.
WebAssembly likely won't be coming to the Beta channel or the stable channel anytime soon. Since it has been in development for years already, there is likely still plenty of work that needs to be done on it before it can be made available for the masses that use Chrome everyday. Since this is handling how some background processes work in Chrome, it's a bit tougher to work on, than say a new user interface would be.