The employment of modern technologies is widespread in our society, so the inclusion of practical activities for education has become essential and useful at the same time. These activities are more noticeable in Engineering, in areas such as cybersecurity, data science, artificial intelligence, etc. Additionally, these activities acquire even more relevance with a distance education methodology, as our case is. The inclusion of these practical activities has clear advantages, such as (1) promoting critical thinking and (2) improving students’ abilities and skills for their professional careers. There are several options, such as the use of remote and virtual laboratories, virtual reality and game-based platforms, among others. This work addresses the development of a new cloud game-based educational platform, which defines a modular and flexible architecture (using light containers). This architecture provides interactive and monitoring services and data storage in a transparent way. The platform uses gamification to integrate the game as part of the instructional process. The CyberScratch project is a particular implementation of this architecture focused on cybersecurity game-based activities. The data privacy management is a critical issue for these kinds of platforms, so the architecture is designed with this feature integrated in the platform components. To achieve this goal, we first focus on all the privacy aspects for the data generated by our cloud game-based platform, by considering the European legal context for data privacy following GDPR and ISO/IEC TR 20748-1:2016 recommendations for Learning Analytics (LA). Our second objective is to provide implementation guidelines for efficient data privacy management for our cloud game-based educative platform. All these contributions are not found in current related works. The CyberScratch project, which was approved by UNED for the year 2020, considers using the xAPI standard for data handling and services for the game editor, game engine and game monitor modules of CyberScratch. Therefore, apart from considering GDPR privacy and LA recommendations, our cloud game-based architecture covers all phases from game creation to the final users’ interactions with the game.