It most certainly is a game animal and the giraffe family has yielded many other game animals over the past 50 million years. If you're saying that it shouldn't be hunted even though its a game animal, that's a different debate. But arguing that the giraffe isn't big game is like arguing the sky is not blue. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.