It would mean (I don't know what the truth is here - and neither do you...) the same thing to OpenGL... DirectX is used for Xbox games, Windows games, Windows Phone 8 games today, already. Throw Unity into the equation and then you move further up the ease-of-use stack. This is actually more interesting in context.
WebGL doesn't replace or supplant the need to use OpenGL. Same is true for DX. WebGL is a browser-targeted technology. WebGL, asm.js, OdinMoney, etc... are not as fast as native code.
There's always a larger runtime overhead and then there's the GC (not that reference counting doesn't have its weaknesses). There is no way around that unless the underlying system is inside the runtime (is the runtime). Mozilla is shipping an HTML5-based mobile operating system, so this means more to them, right? Well, then there's ChromeOS.
We too often declare the end of technologies when a new (often related) one emerges.