I look it up the "Collins English Dictionary",this book defines "a gamekeeper is a person who takes care of the wild animals or birds that are kept on someone's land for hunting".So you can see, there are a lot of need to protect the magic creatures in the Dark Forest, and J.K.Rowling use the gamekeeper to describe the Hagrid's position.
by the way, I'm Chinese, so I just do my best, hope it can help you.