Yes, it can apply to classless games
The primary, deeper exercise of answering multiple questions does not rely on class at all, and is intended for players or characters. The section involving classes is just a table suggesting a specific single question to use as a starting point for establishing character relationships. It does so by “type” rather than explicit classes.
The types are:
- Warrior/Melee Combat
- Priest
- Magic-User/ Ranged Support
- Magic-User/ Ranged Attack
- Rogue / Black Ops
- Specialist - Tinker/ Technologist
- Iconoclast
- All-Around / The Face
While these match up with the common fantasy archetypes or roles found in classes, they are not at all mechanically linked to those classes. The text refers to using these types as “preferred descriptors”, so for a classless game, match up your characters to the “types” that most closely match their personality and skills.
For Mouse Guard or Call of Cthulhu (or any game where fitting into those types might be a little harder), you could also imagine your investigators or mice playing the equivalent of Dungeons & Dragons, and choosing the character type they feel would suit them best. (This can be a fun character creation exercise all on its own, by the way, and often helps players who are used to class-based games.)
Alternatively, you could also select a question that seems appropriate, or roll for one randomly. The three spheres and their individual questions are numbered for this purpose.