The only way around it, is to use a target SDK of 22 or lower. In which case the permissions will be requested at install. Note that you will not be able to distribute your app through the play store with a target Sdk lower than 26.
If the device is running Android 5.1 (API level 22) or lower, or the app's targetSdkVersion is 22 or lower, the system asks the user to grant the permissions at install time.
The camera permission is a dangerous permission.
Check for permissions
If your app needs a dangerous permission, you must check whether you have that permission every time you perform an operation that requires that permission. Beginning with Android 6.0 (API level 23), users can revoke permissions from any app at any time, even if the app targets a lower API level. So even if the app used the camera yesterday, it can't assume it still has that permission today.
The app you reference asks for runtime permissions.
This answer discusses the possible abuse of Android permissions. It's something that needs to be reported to Google.