My favorite rifle for hunting out west for deer and antelope was a standard Remington 700 BDL in .270 Win. I've taken game with it from 10 yards to over 400. That rifle was flat out accurate. Like a dummy I went and sold it and regret it every day.
So to answer your question: NO you don't need a "special" long range rifle. Find a load your rifle likes, practice and use it with confidence.