OpenGL and DirectX aren't languages - they're APIs. You could try to RPC them, but in all honesty you'll want to add a layer and use a real language designed to stream the information to the user.
The underlying language used is likely to be something like X3D or some other language designed for streaming over the Internet, which won't care if it's being rendered using DirectX or OpenGL.
. . . and in all honesty, I'm just not seeing much in the way of 3D coming to the Internet in any big way. 3D for the Internet has actually been around for a long time: We had VRML since before 1995.
Problem is, there's no demand for it. I don't see any big push for 3D in a browser. Hard core gamers are perfectly happy downloading games or using downloadable clients. Casual gamers are fine with 2D Flash games.
OpenGL vs Direct3D are just different ways of rendering. It's like saying we're having a contest between WPF (Windows), X Window (Linux), and Cocoa (Mac OS) for the Internet.
What's used for the final rendering won't really matter as much as the languages used to communicate between the server(s) and the client(s).
What I think may happen if we get more 3D is that it'll be done through an update of an existing common plugin such as Flash, Silverlight, or Java.
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