I really regret the number of things we're allowed to casually refer to as "harm". That word used to be significant to me but now carries very little weight, manifesting instead as inconvenience, frustration, or, in this case, distraction.
One of the definitions of harm is: "actual or potential ill effect or danger"
This does have a potential ill effect: students playing games instead of following along with the lesson.
The teacher isn't being harmed, but the student's education is being harmed.
If teachers can be so boring that the t-rex game outcompetes them for the attention of students then the problem is teachers not the game.
I understand that not al teachers can be like Richard Feynman or Tatiana Erukhimova or Walter Lewin but surely we should expect them to be better than the t-rex game.
Many schools have wardens instead of teachers.
The only class that might be able to be made more interesting is English. The Scarlet Letter and The Great Gatsby are both snoozefests. But for other subjects the idea of "creating engagement" is more difficult. People seem to think children possess the foresight they do even though they are adults. In middle school, most of the time you can just say "this will get better in a few years if you do well here". Children lack a sense of delayed gratification. Hence the popularity of PE as a subject (aside from the health benefits) or music classes relative to other classes. Funny enough, the modern adult (still a child) also tends to lack this ability. There's nothing wrong with these classes intrinsically. They just provide an "instant" dopamine hit a developing brain is hardwired to understand.
Not everyone can afford to send their kids to a "montessori" school to have some avante garde teaching method keep them "engaged". For the rest of us, learning how to cope with something boring will be an extremely useful life skill the second you enter the real world.
School, as it currently exists, may be boring. I remember being bored out of my mind; that didn't necessarily need to be so though. Many teachers read out of our books and could explain little else beyond the content of the book. I hated maths and Spanish as a result. Many of the teachers attracted to these subjects aren't the kind of people who should be teaching kids. Meanwhile, when I learned Chemistry I learned more about maths than I could've ever dreamed and I was captivated.
As an adult I relearned a lot of that math to succeed as a programmer and it was fun. I think, largely, we fail to meet students where they are with respect to their education. We shove everything down their throats on our schedule rather than the pace in which they can build on these subjects. The result is boredom derivative of disenchantment.
I'm not even sure what your point about Montessori education is. The teachers do not make it special. The method is what's special, which is that pace is dictated by the pupil.