Your understanding is correct, you should be able to see HID keyboard in the Bluetooth settings...getting it to work is another story.
When you figure it out, please let me know! It was one of those examples that when I started with the CC2540 only led to frustration.
I would highly recommend you leave this project until you get a better understanding of BLE. Try all the other examples that connect to the BLE MultiTool, SENSORTAG or other free apps that work. Once you start with HID, the first thing you will notice is that the buttons are for left and right arrows. Well, there are no such arrows on iOS.
You never know though, you could be the one to figure it all out!
Take my advice, start with the Keyfob and a free App, BlueRadio is also a good one, and proceed from there. There are a lot of smashed KeyFobs and Debuggers under plenty a programmers feet!
Thanks,