The use of game-based digital medicine is gaining increasing interest in helping children with ADHD to improve their attention outside the clinical setting. In this process, it is important to continue monitoring children's responses to the use of digital medicine. In this work, we introduce novel digital markers and an analytic pipeline to estimate ADHD-related symptomatic levels during the self-administration of attention games. The digital markers, capturing the children's characteristics of attention and inattention spans, were extracted and translated into clinically-accepted measures of ADHD symptoms, specifically the ADHD-Rating Scale (ADHD-RS) and Child Behavior Checklist (CBCL). To validate the feasibility of our approach, we collected game-specific performance data from 15 children with ADHD, which was used to train machine learning-based regression models to estimate their corresponding ADHD-RS and CBCL scores. Our experiment results showed mean absolute errors of 5.14 and 4.05 points between the actual and estimated ADHD-RS and CBCL scores respectively. This study enables new clinical and research opportunities for accurate longitudinal assessment of symptomatic levels of ADHD via an interactive means of playing mobile games.