Can an employer require me to watch training videos on an unpaid break

If it is mandatory you should get paid for it. It is training while on the job after employment started. You should get paid in my opinion. You may call the wage and hour division of the department of labor at 1000 east grand in Des Moines and ask if you want clarification.

I'd strongly question whether as a matter of wage or, if applicable, overtime law this is legal. Arguably the training video is mandatory and benefits your employer. Thus the training video time should be considered compensable working time.