Individuals with permanent cognitive impairment need to be evaluated and monitored. There exists a number of clinically validated cognitive assessment tools, but they often need to be administered by trained therapists in clinical settings. This serves as a major barrier for frequent, longitudinal monitoring of cognitive function. In this work, we introduce Neuro-World, a series of innovative 3D mobile games, that allows one to self-administer the assessment of his/her cognitive function. The game performance is analyzed and converted into a clinically-accepted measure of cognitive function (i.e., the Mini Mental State Examination (MMSE) score), improving the translational impact of the system in real-world clinical settings. To validate the feasibility of our approach, we collected game-specific performance data from 12 post-stroke patients, which was used to train a supervised machine learning model to estimate the corresponding MMSE score. Our experiment results showed a normalized root mean square error of 5.3% between the actual and estimated MMSE scores. This study enables new clinical and research opportunities for accurate longitudinal assessment of cognitive function via an interactive means of playing mobile games.