Is there any way to play Unity games that were released as only a .exe have not been updated to include a UnityPlayer.dll in the download?

You can't; it's impossible.

All standalone Unity executables always come with a XXX_data (assuming the executable is XXX.exe, and replace XXX with the name of the game).

I've looked at the game download files and the folder/executable pair is there. Did you maybe incorrectly extracted the zip file?

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