Nope, see if this helps.
When the ball is being thrown back to the pitcher or being “pitched” to the catcher there is no “play” going on. The ball is “live” yes. But no one would define those two instances in the most commonly used, and accepted, definition as a “play”. Once the batter hits the ball or there is some kind of errant throw by pitcher or catcher than the someone has to make a “play” on the ball.
Some are trying to apply a very legalistic and not necessarily accurate view of the use of the word “play” in the baseball code. Many, many, MANY words are found in the “law” that have a definition applied to them there that the overwhelming number of people would not apply to them and they would apply a different, more commonly accepted and used definition to them. Doesn’t make either of them “wrong”. But using the “legalistic” definition in the case of my post IS wrong.
In my original, theoretical situation I posted to start this thread the definition of the word “play” is not the one found in the “law” of baseball cited.
It is an unusual characteristic of baseball that it is the defense - the pitcher - who initiates. The batter can’t club a low, inside fastball into the middle of next week when the pitcher elects to throw a change up. It is the pitcher who starts all plays - not the batter, who is in a real sense on defense trying not to be called out on strikes (if he does nothing, and the pitcher gets the umpire to call three strikes) or otherwise hit the ball where the defense can make a play on him, or on one of his teammates on base.
I recall once standing behind the rubber waiting for the next batter to stand in, and thinking, “It’s really nice of all these fellows to come here so I can have a game.” The pitcher really is that important to a team. Believe me, if your pitcher can’t do his job well the game will be no fun at all.