This paper presents the guidelines for game experiences integration into Learning Management Systems (LMS) through the IMS LTI (Learning Tools Interoperability) specification. At the same time, it also introduces a dynamic scoring formula, based on a given taxonomy, that goes beyond traditional metrics, allowing for the inclusion of any number of game elements, such as levels, challenges, hints used, and time taken, within the game framework. These elements are assigned weight factors, which can be configured by instructors within the LMS platform, facilitating personalized assessment criteria tailored to specific learning objectives. In order to apply these approach in a real educational scenario, an Escape Room (ER) for math skills testing was used. Using the LTI specification for integration in combination with the dynamic scoring formula provides a comprehensive assessment of student performance, giving a single score which will be vital to enhance the LMS gamified workflow. This research contributes to the field of gamification in education, offering insights into the integration of (serious or regular) games in LMS platforms.