Unity is working on a WebGL exporter which one day will be as ubiquitous as HTML5 (yes, even the latest IE is beginning to support it ;)) so your projects in Unity will work in standard browsers without plugins (probably by the time you have finished it).
Another option is to use the open-source tool which even Unity is using to make this possible, Emscripten allows you to write in standard C and C++ and output to HTML5 (via the wrapped SDL library) or WebGL (via the inbuilt OpenGLES 2 support).
Even Microsoft is suggesting it in their preliminary WebGL docs (http://msdn.microsoft.com/en-us/library/ie/bg182648%28v=vs.85%29.aspx).
I think where you might be hitting a wall is trying to use technologies like CSS. This type of web tech does not offer enough flexibility for pseudo realtime games (I personally also find it completely defective for normal web pages too). So I suggest looking at "coding" languages as opposed to markup (layout) languages.
But yes, I also believe games are going the direction of the web. If only because it allows publishers to "lend" the game to a player rather than allowing them to keep a copy (i.e DRM).
Most tablets are also so locked down and crap, that people can only really use them for the web browser anyway, so games on the "web browser" platform are more convenient for potential players.