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The modern web idea which you are talking about does not really have a specific name (it probably should). I generally try to use backbone.js or ExtJS or the like to do an MVC in the browser and treat the server as a data source that can have its own logic as well.
Don't worry so much about what it is called as much as how to write good code and make something that does the job.
I call that "web app" development or "fat client" where you are including all your GUI interactivity on the client-side and the server is only providing data. MVC is more akin to "Enterprise Web Applications" or as I call them "pretentious layers of software".