Individuals with cognitive impairments are evaluated using clinically validated cognitive assessment tools, which need to be administered by trained therapists. This serves as a major barrier for frequent and longitudinal monitoring of patients' cognitive impairment level. We introduce Neuro-World, a set of six mobile games designed to challenge visuospatial short-term memory and selective attention, which allows one to self-administer the assessment of his/her cognitive impairment level. Game performance is analyzed to estimate a widely accepted clinical measure, the mini mental state examination (MMSE), which highlights the translational impact of the system in real-world settings. We collected game-specific performance data from 12 post-stroke patients at baseline and a three-month follow-up, which were used to train supervised machine learning models to estimate the corresponding MMSE scores. The results presented herein show that the proposed approach can estimate the MMSE scores with a normalized root mean square error of 5.75%. We also validate the system's responsiveness to longitudinal changes in cognitive impairment level and demonstrate the system's positive usability in cognitively impaired individuals and their willingness to adhere to the longitudinal use. This study demonstrates that Neuro-world has great potential to be used to evaluate the cognitive impairment level and monitor its long-term change. This study enables new clinical and research opportunities for accurate, longitudinal assessment of cognitive function via mobile games.