(1) Background: Throughout the history of medical and psychology practice, specialists have worked to improve the quality of treatment and rehabilitation, which has led to the emergence of concepts such as serious games. These tools focus on different areas of intervention procedures, one of which is to help people with intellectual disability (ID). Individuals with ID have problems with executive functions (EFs), which are related to adaptive functioning. Recent studies showed that serious games positively impact cognitive, social, and communication skills in people with ID. The purpose of this study is to analyze the solutions that have been found in EF training for adults with ID in recent years, evaluating them with a number of key parameters and identifying the features and possible problems in the further development of our system. (2) Methods: A review was conducted starting with 573 articles in English related to serious games and selected from studies that had been published since 2015. Finally, 10 were examined in detail as they focused on EFs in adults with ID. They were searched in seven major databases (“Association for Computing Machinery” (ACM), IEEE Xplore database, DBLP computer science bibliography, Google Scholar, PubMed, SCOPUS, and PsycInfo). (3) Results: It was determined that the most frequent EFs referred to in the studies analyzed were planning and decision-making, followed by working memory and social cognition, behavioral regulation, flexibility, and inhibition capacity. The basic approach to the creation of support systems was also analyzed in terms of technical and program execution. The trend results’ analysis evidenced improvements in EFs, even though they were not significant. This comprehensive technique enabled the identification of the main features and aspects to be taken into account for further development of our system.