When a user has permissions to "Report Suite Tools > Report Suite Mgmt" and "Report Suite Tools > Classifications", they are able to configure Classifications, Import/Export them, and Manage Classification Rules. This does not require to be a product admin.
However, there is a security issue that presumably is not widely known (or is not considered an issue by the product team) — the user gets access to all report suites in the Classification Importer and Classification Rule Builder.
I have tried testing your scenario by creating a new product profile with access to the report suite followed by the permission as shown below.
You can try creating the product profile with similar permissions as well. Also, I can confirm that to access the Classification Importer & Classification Rule Builder, you will not need to provide Analytics Product Admin access to the users.
If the question is around accessing Classifications in the report suite settings, that's possible by a non-Admin user. However, it's not possible to access Classification Importer/Rule-Builder by a non-Admin - that's my understanding, unless I'm missing something.