Privacy and Google Apps for iOS
After you install any of the apps published by Google on your iPhone, it can determine whether you have the other Google apps installed on your iPhone by using the following API call available in iOS:


canOpenURL: - UIApplication


Based on this, it could be determined what apps you do not have installed on your iPhone, and Google can suggest you to install them.

An iOS app can be assigned a custom URL scheme by it's developer. It's using URL scheme that your iPhone is able to directly launch say for e.g. YouTube or Google Maps app if link for the same is tapped in any of the other apps.

This specific instance isn't necessarily a privacy violation as Google is simply using one of the APIs made available by Apple. When it comes to apps, Google is just another 3rd-party app publisher on iOS and has to adhere to same privacy restrictions like every other developer.

P.S.: While it could be argued that Google's privacy stance is not as strong as Apple, they are bound to adhere to restrictions imposed by Apple as they are no different from other 3rd-party app developers for iOS and generally do not get any elevated privileges.