The impression I got is that it's not a successor to MVC so much as a complement, for example figure 5 in the artima article on DCI has both. I think it's supposed to help make the distinction between model and controller more sane, or maybe between different part of the controller or different parts of the model.
The basic idea seems to be to split logic for particular actions our of your data classes and move it to traits/mixins/whatever, one per (user) action. You'll have many small pieces of code, instead of a few large pieces. Also, it sounds like adding new mixins is supposed to be "better" than adding functionality to your base classes. The code for individual actions will probably (I think?) be more spread out, but code for different actions should be more clearly and obviously separated.
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