While good advice, having the debug version of adobe flash player or one of the standalone replacement players from gamesites in your game folder and dropping those beloved old flash games on it, is not installing flash.
Back then, if you had flash installed it was automatically activated for stuff you viewed in your browser. So they could use that for all sorts of shenanigans, even pseudo cookies.
I wonder if there even are some sites left where those shenanigans are used at all. Since flash is dead, it would be a waste of time to inlcude it in a website.