Designing educational games is a complex task and needs collaboration between game developers and an educator. Domain-Specific Modeling Language (DSML) offers an approach to simplify the design activities of educational games and support the involvement of both game developers and educators. This paper presents an extension of Serious Game Logic and Structure Modeling Language (GLiSMo), a DSML that designs the logical and structural views of educational adventure games. The gap in the original GLiSMo is that it did not allow an educational game to be designed according to any learning theories. Furthermore, the original GLiSMo does not cover all concepts in the adventure genre. The authors intend to extend the original GLiSMo by adding the concepts of Flow Theory and concepts of the adventure genre to make it more expressive. The extended DSML is called FA-GLiSMo. The authors evaluated the expressiveness of FA-GLiSMo using Framework for Qualitative Assessment of DSLs (FQAD). The result shows that the expressiveness of FA-GLiSMo is still 'incomplete' due to the lack of clarity of semantics for several domain concepts. Improvements were performed, and the finalized FA-GLiSMo now has fifteen (15) concepts of the Logic diagram, nineteen (19) concepts of the Structure diagram, and a new diagram called the Flow diagram containing five (5) concepts of the Flow Theory. The authors also demonstrate in this paper the concrete syntax of FA-GLiSMo using the Tales of Monkey Island game as a case study.