Unity, Flash and Shockwave needs to be killed off for good.
Well, good news on one front: Unity Webplayer is officially end-of-life as of last year, and webplayer authoring is not supported at all in the recent 5.4 release of Unity. When it comes to browser gaming, Unity is focused 100% on cross-platform, open standard HTML 5/WebGL, and is working closely with Mozilla on bringing those technologies up to par with native.
(Outside browsers, Linux is a first-class Unity target platform, and the Linux version of the Unity editor is coming along nicely, although it's still considered experimental.)
Full disclosure: I work for Unity Technologies.