I've considered linking you materials such as the etymology of the word, the various current dictionary and encyclopedia definitions, even philosophical treatises on the subject of games. I also considered a more practical approach, quoting examples from culture like film, literature or actual children's or folk games. This would end it factually for anyone with a charitable approach to communication but since any of these are pretty easy to look up and yet you either haven't or have chosen to reject them, I decided against it.

I do have the feeling that you are aware of them. That it's not as if you don't know that a great many people understand the word different from you. It's more that you think they are all wrong and it is only you that truly understands the word. So let me instead ask you what it is that you have learned about the nature of games that, given this abundance of support of a less reductive definition, it is yours that is exclusively correct and people should go find new names for all these other things.

I'm trying to keep an open mind, but please let it be something more thought out than "everyone should model their mind maps after my own".

Edit: Attempt to unsnark a little.