The flight instructor in the retractable, landing gear-equipped airplane reported that the pilot receiving instruction was on the controls and that he told the instructor that he was feeling some motion sickness due to light turbulence in the pattern; the pilot corroborated the instructor's statement and stated that he was also fatigued. The instructor reported that, during their discussion, they became distracted and did not configure the airplane for landing; the pilot reported that they did not complete the landing checklist. Subsequently, the airplane landed with the landing gear retracted. The airplane sustained substantial damage to both engine gear boxes. The instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.