I can’t diagnose a child on the basis of a letter, of course, but I can tell you that this little girl needs an evaluation. I understand why your sister doesn’t want to think something is wrong. No mother does. But what you report is not usual behavior in a five year old.
Within the diagnosis of autism is a huge range of behaviors. That’s why it is called an “autism spectrum disorder.” One thing kids on the spectrum seem to have in common is sensory issues. Many react strongly to smells, sounds, sights, etc. that wouldn’t bother other kids. Often there is some element of what looks like obsessive-compulsive type behavior. (It’s unclear whether this is really OCD or an artifact of autism itself.) Your niece’s “rules” about puzzle pieces and how you need to make things with play-doh to be “right” may fit. On the other hand, there may be something else going on. Kids develop unusual behaviors for all kinds of reasons.
All I can tell you for sure is that you are right to be concerned and that this little girl needs to be evaluated by a qualified clinician as soon as possible. Early intervention is key to helping kids with autistic leanings to learn how to master their own behaviors. If she is on the autism spectrum, every month that she goes without treatment is a lost opportunity to help her. If, on the other hand, she is acting out some other kind of hurt, it’s important to know that so that you can provide the right kind of support.
I hope you can talk candidly with your sister. I understand completely why she doesn’t want to hear that something is wrong. But loving her daughter means getting the information she needs so she can be helpful.
I wish you well.