The ability to archive issues is restricted to those with the proper permissions. The design language of Jira will generally remove options or sections of the product that a user does not have the ability to access.

In this case, users without global/project admin or archive issue permissions are still able to see the archive issue option when right-clicking an issue within a board:

While they are not able to archive the issue, users are prompted to elevate their permissions:

The option to archive is removed from the issue detail view for these users.