For anyone interested in its claim of being reactive, as I was, the Play framework does not appear to support reactive programming [1].
From their samples and documentation, it looks like an event-driven server without any reactive aspects. I'm fairly sure they're mistakenly calling typical event-driven programming "reactive". This is backed up by the statements of Typesafe's CEO on the subject in an interview [2].
Which indeed is talking about stream processing. Play's stream processing uses iteratee IO to correct control inversions often suffered by networking libraries.
However, Play does not offer automatic facilities for having variables (and interface) update when other variables change, as described in the Wikipedia article. For examples of reactive programming, see Knockout, batman.js and Ember.js (all primarily client-side).