Jelena,
So you are using the GAME plugin for Moodle. I have used that too. I now ask the students to help design the game. I proved a brief introduction and showcase to provide context then I set up a glossary and give them a topic to research. Everyone is given a set time to add a new concept and definition in the Moodle glossary. After (say 20 minutes) I add a new Snakes and Ladder game based on this glossary.
It really changes the class engagement because they know their mates are going to be reading their work. They put more thought into it and know that they will be held accountable. I am often asked if games and play make learning 'too easy and fun' yet, the way I use them, it increases the difficulty level and accountability. They like the challenge and I like the amount of reflection involved,as that is where the real learning takes place.
What do you think it is about using these games that your students like? Perhaps you could ask them.