The deficit in social interaction skills among individuals with autism spectrum disorder (ASD) is strongly influenced by personal experiences and social environments. Neuroimaging studies have previously highlighted the link between social impairment and brain activity in ASD. This study aims to develop a method for assessing and identifying ASD using a social cognitive game-based paradigm combined with electroencephalography (EEG) signaling features. Typically developing (TD) participants and autistic preadolescents and teenagers were recruited to participate in a social game while 12-channel EEG signals were recorded. The EEG signals underwent preprocessing to analyze local brain activities, including event-related potentials (ERPs) and time-frequency features. Additionally, the global brain network's functional connectivity between brain regions was evaluated using phase-lag indices (PLIs). Subsequently, machine learning models were employed to assess the neurophysiological features. Results indicated pronounced ERP components, particularly the late positive potential (LPP), in parietal regions during social training. Autistic preadolescents and teenagers exhibited lower LPP amplitudes and larger P200 amplitudes compared to TD participants. Reduced theta synchronization was also observed in the ASD group. Aberrant functional connectivity within certain time intervals was noted in the ASD group. Machine learning analysis revealed that support-vector machines achieved a sensitivity of 100%, specificity of 91.7%, and accuracy of 95.8% as part of the performance evaluation when utilizing ERP and brain oscillation features for ASD characterization. These findings suggest that social interaction difficulties in autism are linked to specific brain activation patterns. Traditional behavioral assessments face challenges of subjectivity and accuracy, indicating the potential use of social training interfaces and EEG features for cognitive assessment in ASD.