Some generators are indeed ungrounded. It works in the same way an isolation transformer does. (This is also known as an IT system.)
This means that the first fault to ground that appears does not have any dangerous result. It only grounds whatever wire that came into contact with the ground. The danger is a second fault on the other "leg". You could have two pieces of equipment with full mains voltage between the the cases.
Therefore, the ground wire is still very important: In case of a second fault, the current will flow between the two faults in the ground wire. This will of course the breaker. (It's a bit more complex if you have a large system, but this is just a small portable generator)
A grounded extension cord will protect you even if the socket at the generator lacks ground.
Honda must have done some trick to get a GFCI to work on a system of this type. Is there a ground rod?
