Can I pick and choose which game apps to transfer with progress instead of all the apps I have?
How to transfer selected game apps with its progress from iPad to iPhone?
iPad, iOS 10
Unless your game uses iCloud storage to save game progress, or has a cloud-based account provided by the game Developer within which to save your progress, your options are limited.
If the game uses iCloud to save progress, you should find a corresponding App setting for iCloud - which you should ensure is enabled for each of your devices:
Settings > [Your Name / AppleID] > iCloud
Scroll down the list of Apps, looking for the your game; if found, ensure that the setting is enabled on each device.
Otherwise, you might be best advised to seek assistance from the Game Developer: