If you're wondering on how to play the game, or you managed to run it but the New Game button is broken, i've made a guide:
Guides -> https://www.speedrun.com/elephant_quest/guide/d98t4
As far as i know, Newgrounds Player cannot run Elephant Quest by itself, this is what i do:
You need to install Flashpoint (I personally use Flashpoint Infinity 11.1), you can do so right here: https://bluemaxima.org/flashpoint/downloads/ From here you can play Elephant Quest by searching up the game, you need to run it, start a new game, skip the intro and let the world map load. Then you close it, and reopen from Newgrounds Player, everything should work fine now.
Everytime you restart the PC, you have to do this again, i don't recommend using .swf files because the borders are broken, just start it from the page: https://www.newgrounds.com/portal/view/566862
I suspect all of this is caused by an uncompatibility with ActionScript 3 (???) so by starting the game from Flashpoint, everything gets loaded and then you can play from Newgrounds Player. Of course you can just play from Flashpoint, but i like NG more because it has way less lag.
I'm probably going to make a thread about this.