Apps don't run as users, users run as users. If you install an app into Program Files, and let's assume you needed elevated permissions to do so, when your standard user then runs that app, that is the user that needs permissions.
- App is installed with elevated permissions (user: Admin, for example)
- All permissions on the AppName folder might well be "Admin:Full, Users:Read"
- User runs app, so cannot change any files
At install-time, your installer will need to know which of it's own files need to be made writable to standard users, and set permissions accordingly. Of course, user-data should not be in Program Files anyway. That's what %appdata% and the user profile are for, usually.
If your app has a globalsettings.ini or whatever, that lives in "Program Files\YourApp", then while you have admin permissions (i.e. at install time) you need to grant write permission to all users to that globalsettings.ini file. Or Power Users. Or a group. Or whatever is correct for your app.
In summary, no, users do not have default write-access to ProgFiles, nor should they.