They're unrelated. Wheel of Misfortune is just a role-playing replay of a previous incident as a training exercise. Someone will grab (or simulate) logs and dashboards from the incident and then play GM for the wheel of misfortune at a future team meeting. Someone who isn't familiar with the incident will be designated "on-call". They'll state what they want to do and the GM will tell them or show them what they see when they do those things.
Chaos Monkey is actually taking down production systems to make sure the system as a whole stays up when those individual pieces fall. Google does have (manual, not automatic) exercises doing similar things called DiRT (Disaster Recovery Testing), but it's not related to the SRE training exercise.
(standard disclaimer: Google employee, not speaking for company, all opinions are my own, etc.)
Chaos Monkey is actually taking down production systems to make sure the system as a whole stays up when those individual pieces fall. Google does have (manual, not automatic) exercises doing similar things called DiRT (Disaster Recovery Testing), but it's not related to the SRE training exercise.
(standard disclaimer: Google employee, not speaking for company, all opinions are my own, etc.)