P.M.
Hitting and overhand throwing are a completely natural developmental stage for babies. They are compelled to do it, and it is helping her increase her eye-hand coordination and gross motor skills. To her, it probably does feel like a game.
I would re-direct. Give her targets to throw things at or into. Give her a soft object, like a particular pillow, to hit. When she starts hitting, say, "We don't hit people (or pets). Here, let's hit this pillow!" And then giggle along with her as you help her pound the heck out of it. This worked well for my grandson when he was in that 4-month-long stage. But it did take frequent reminding what the acceptable targets were.