Multi-modal large language models (MLMs) are often assessed on static, individual benchmarks -- which cannot jointly assess MLM capabilities in a single task -- or rely on human or model pairwise comparisons -- which is highly subjective, expensive, and allows models to exploit superficial shortcuts (e.g., verbosity) to inflate their win-rates. To overcome these issues, we propose game-based evaluations to holistically assess MLM capabilities. Games require multiple abilities for players to win, are inherently competitive, and are governed by fix, objective rules, and makes evaluation more engaging, providing a robust framework to address the aforementioned challenges. We manifest this evaluation specifically through Dixit, a fantasy card game where players must generate captions for a card that trick some, but not all players, into selecting the played card. Our quantitative experiments with five MLMs show Dixit win-rate rankings are perfectly correlated with those on popular MLM benchmarks, while games between human and MLM players in Dixit reveal several differences between agent strategies and areas of improvement for MLM reasoning.