Based on the picture, I gather that the "pitcher" uses the plunger at the base of the machine to launch the ball up and around so that it comes out the hole in center field.
The "batter" then uses the bat-like flipper to hit the metal ball. Where ever the ball ends up determines the outcome of the play.
I've seen a few of these online. This one seems to have a few more ramps, holes, and details than the others.
From Back to Basic Toys:
"Award Winning Old Century Baseball....Crafted with aged woods and metals, this exquisitely detailed pinball-style table top game pays homage to those golden years of baseball... Use the flippers to hit doubles, triples, and homers; scoreboard and score book let you keep track of the action! Comes with three marble-sized steel balls. Size 21"l x 22"w x 12"h."
You can also upgrade your machine to feature the Major League team of your choice on the scoreboard. I wish they had obscure retro Minor League team names too.
Check out the Old Century Baseball pinball style baseball game.