From what I've read about other Samsung devices, I don't think the Gmail app has an unread count badge if you're on stock TouchWiz. You'd have to install something like Unread Badge (for Gmail), or install an alternate launcher that supports unread count badges on more icons (like Nova Launcher).
With TeslaUnread you can enable notifications to almost any App and can customize it to your liking. If you have installed Nova do give TeslaUnread a try.
Sometimes you have to be persistent. Send them a couple of followup emails. At least we know that the developer is still paying attention to the app, since the last update was 8/4/16.