I’m by far not an expert on it (my wife is, she teaches Montessori), but AFAIK what you observed was because it isn’t viewed as play, but as work - as in school work. All of the activities are called “works,” and they’re taken very seriously.
Part of this is, I think, to teach responsibility; for example, if a student gets a work out, they’re expected to put it back exactly how they found it. Montessori classrooms are incredibly well-organized, with everything having its (labeled) place.
Update: I asked my wife, she said that without other context, it sounded like the school may not be “following the child,” a core tenet of Montessori. She said that while they might steer a new student away from that initially, if they’re clearly interested, she’ll bump that lesson up early instead of when it was scheduled.
