Originally Posted by mineistaken

At least at that time when you hit those balls you are a player, because you play.

Take another example - driver. If you drive a car you are a driver. You do not need to be professional driver to be called a driver.

Or better example - monopoly player. You may be the first time player but if you sit at the table playing monopoly you are monopoly player.
Somebody: Players, roll the dice!
You: Hey, I am not a player, I just play.
NO. You are a player
Same with baseball. You went the wrong route just because you are used to use "baseball player" term when speaking about pros etc. But like you see from monopoly example - you are 100% a player if you play.