To be safe, yes. I would have to dive into the code to make sure it was necessary (which you can do as well since the code is provided). What it means when it says this library isn't thread safe is that any globals, file access, etc. are not protected with synchronization objects to prevent simultaneous access. There could be globals inside this library that you would need to protect and therefore should only use the Ini functions from one thread at a time using thread locking, or one thread only.
Chris