Creativity assessments should be valid, reliable, and scalable to support various stakeholders (e.g., policy-makers, educators, corporations, and the general public) in their decision-making processes. Established initiatives toward scalable creativity assessments have relied on well-studied standardized tests. Although robust in many ways, most of these tests adopt unnatural and unmotivating environments for expression of creativity, mainly observe coarse-grained snippets of the creative process, and rely on subjective, resource-intensive, human-expert evaluations. This article presents a literature review of game-based creativity assessment and discusses how digital games can potentially address the limitations of traditional testing. Based on an original sample of 127 papers, this article contributes an in-depth review of 16 papers on 11 digital creativity assessment games. Despite the relatively small sample, a wide variety of design decisions are covered. Major findings and recommendations include identifying (1) a disconnect between the "potential" of scaling up assessment of creativity with the use of digital games, and the "actual" reach achieved in the examined studies (2) the need for complementary methods such as stealth assessment, algorithmic support and crowdsourcing when designing creativity assessment games, and (3) a need for interdisciplinary dialogs to produce, validate and implement creativity assessment games at scale.