I just added the google-play-services-lib library to my project and am stuck where I need to \"sync the project with gradle files\", but this button does not exist
google-play-services-lib
The Gradle sync is still there, under Tools -> Android -> Sync with Gradle
If you don't see it, then Intellij needs to re-link your gradle file.
Try closing the project, re-opening by File -> Import Project -> and select your .gradle file