

This is probably as valid an interpretation as the more technical ones presented in the other answers and the overall title is likely using that ambiguity for evoking meaning on multiple levels this way, just as the story itself juxtaposes Turing's personal problems with his historical achievements. (As a side-note, the subtitle to the German version of the movie, "Ein streng geheimes Leben" ("A top secret life"), while maybe a little bit too much on the nose, emphasises this connection further.)

So he himself is forced to play an imitation game, imitating a straight man. Turings team, including Joan Clarke (Keira Knightley), analyze Enigma messages while he.

In fact a big emphasis of the movie, beyond the WWII spy story that already offers many possibilities for "imitation", is the rather personal story of Alan Turing and his struggles with being homosexual in a time where that wasn't really accepted at all. THE IMITATION GAME Written by Graham Moore Based on 'Alan Turing: The Enigma' By Andrew Hodges. The other answers already draw some really good connections to various parts of Turing's work, be it movie-related or more general.
