From the beginning of the history of AI, there has been interest in games as a platform of research. As the field developed, human-level competence in complex games became a target researchers worked to reach. Only relatively recently has this target been finally met for traditional tabletop games such as Backgammon, Chess and Go. This prompted a shift in research focus towards electronic games, which provide unique new challenges. As is often the case with AI research, these results are liable to be exaggerated or mis-represented by either authors or third parties. The extent to which these game benchmarks constitute "fair" competition between human and AI is also a matter of debate. In this paper, we review statements made by reseachers and third parties in the general media and academic publications about these game benchmark results. We analyze what a fair competition would look like and suggest a taxonomy of dimensions to frame the debate of fairness in game contests between humans and machines. Eventually, we argue that there is no completely fair way to compare human and AI performance on a game.