Because it is Americas pastime.
1. It's America's pasttime
2. They have fun
3. They can only play it if there's a thunderstorm, if they play without a thunderstorm the humans might wonder what the noise is and expose the vampires of their immorallity, then the vampires will have to kill the human (humans) becase the humans might tell more humans and soon they would overrule the vampires.
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The above is about Twilight. If you like fiction, then that's okay, by all means believe it.
But vampires play Baseball for one reason: because it's fun.
And maybe as a competitive thing.
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A baseball bat, a baseball, a field, a glove, and players, just like everyone else does.
And they need a thunder storm, so as not to be heard by other people.