You will not be able to download the app once it is removed from Play Store, which means you can't install on new phone (and will not be available in your account "My Apps and Games", since it is not available on Play Store). So it doesn't matter whether your phone is old or new- even on your current phone, if you uninstall it , you can't install from play store, if the app is removed from Play Store
Availability
Some apps and games can be removed from Google Play by a developer or for policy reasons. If an item has been removed, it won't be available for download.
Source: Google Play Help - I can't find an app or game
That is not the end of world. For starters, you can consider taking a backup of the game apk (of course, no updates from Play Store). Many ways to do this are suggested here - How to take backup of all installed APKs from Phone to PC?
Alternatively, apps and games removed from Google Play Store, may well be available on:
- Alternate sources (possibility of getting updates): see What are the alternative Android app markets?
- Internet: download apk from internet and install (not recommended since you have no way of knowing for sure that the apk is free of malware or adware)