Existing CAPTCHA solutions are a major source of user frustration on the Internet today, frequently forcing companies to lose customers and business. Game CAPTCHAs are a promising approach which may make CAPTCHA solving a fun activity for the user. One category of such CAPTCHAs - called Dynamic Cognitive Game (DCG) CAPTCHA - challenges the user to perform a game-like cognitive (or recognition) task interacting with a series of dynamic images. Specifically, it takes the form of many objects floating around within the images, and the user's task is to match the objects corresponding to specific target(s), and drag/drop them to the target region(s). In this paper, we pursue a comprehensive analysis of DCG CAPTCHAs. We design and implement such CAPTCHAs, and dissect them across four broad but overlapping dimensions: (1) usability, (2) fully automated attacks, (3) human-solving relay attacks, and (4) hybrid attacks that combine the strengths of automated and relay attacks. Our study shows that DCG CAPTCHAs are highly usable, even on mobile devices and offer some resilience to relay attacks, but they are vulnerable to our proposed automated and hybrid attacks.