With the advent of digital personal assistants for mobile devices, systems that are marketed as engaging in (spoken) dialogue have reached a wider public than ever before. For a student of dialogue, this raises the question to what extent such systems are genuine dialogue partners. In order to address this question, this study proposes to use the concept of a dialogue game as an analytical tool. Thus, we reframe the question as asking for the dialogue games that such systems play. Our analysis, as applied to a number of landmark systems and illustrated with dialogue extracts, leads to a fine-grained classification of such systems. Drawing on this analysis, we propose that the uptake of future generations of more powerful dialogue systems will depend on whether they are self-validating. A self-validating dialogue system can not only talk and do things, but also discuss the why of what it says and does, and learn from such discussions.