Q: How can I get an app from my iPhone to my new iPad? Let me explain..

You can't get it on your iPad unless you have it in your iTunes library on your computer. If you have it there, sync it to your iPad. You can try to transfer the game into iTunes and sync it to the iPad, but since app thinning was introduced, I am not sure that this will work for you.

Redownload or transfer your iTunes Store purchases from an iPhone, iPad, or iPod to a computer - Apple Support

A note of caution, if you have never synced with iTunes before, this may turn out to be more trouble than it is worth. Have you synced with iTunes in the past!