We ask for permission to manage your account because we use that ability to read your contacts and make suggestions when you are typing in email addresses to share diagrams or projects from within the Creately app. This is absolutely the only thing we use it for. When we launched the App, Google did not provide a specific API for reading the contact information from Google accounts. It could only be done through the manage permission option.
We are investigating the possibility of changing this to use lesser or more specific permission. And therefore avoid the more generic manage account permission. However, this will take a little time as we need to fit it around our other ongoing work.
For the moment, we suggest you proceed with your purchase and usage of Creately and when the permissions change you should be prompted by Google at a time when you log in to Creately with your Google account.