I am not sure what you mean by your question. I am not a developer, so I do not know if there are many ways to do this/different parameters for it.
I thought there is a standard way to implement group support:
Almost all the core modules and many contributed modules support groups, so that if a module (both Content or Activity) is added to a course that has groups and groupings, you can define access and/or visibility for the module in the interface for editing the module.
If your module supported groups (and, by the way, support for Grade category would also be great!), there would be a section under editing the module (the interface where you choose what game to use, where questions are taken from, game specific settings, etc.) called
"Common module settings"
It would have boxes and choices
- Group mode
- Available for group members only
- ID number
- Grade category
As far as I know (and the title for the section is Common module settings, after all) this is standard interface/parameters for modules. If you look at the Edit/Settings page of any core activity, for example a Quiz, you will see what I mean (you may have to click the "Show advanced" button to see all the options I listed above).
I hope you will implement this, as it is a standard feature for Moodle modules and one that we rely heavily on, as I mentioned in my original post. We really love these games, so it would be a shame if we can't use them!