Valid question. The level of hindrance would depend on the severity/consistency of parental criticism and rigidity displayed towards the child.
If these are just few occurrences here and there, it may not be as detrimental as if this was to be an ongoing treatment.
Play is an important component of the development of any child. You can even see play amongst animals. Through play, children learn about their environment and others. Imaginative play is also important as it allows the child to develop unique problem solving abilities. Experiential play can also be seen as providing the opportunity for social interaction (learning social skills and what behaviors are prosocial).
Very early on, children benefit from play as during play, their developing brain, creates new neural pathways amongst other benefits i.e. motor coordination, problem solving, presenting a creativity outlet, etc.
If the criticism and negative statements are severe and ongoing, what could end up happening to the child emotionally as he/she grows up as a teenager and an adult?