I see in the screen shot that in app purchases are unavailable “check Apple ID in store settings”. That is a user settings issue, it’s not the app itself.
Check your iTunes Store account to make sure the ID info is correct and in app purchases are not disabled, or contact iTunes for help with your account.
Also when you delete an app, iTunes will in many cases require reinstalation approval for each previous purchase. They make it look like they are going to charge you, but they won’t. Just accept the purchase, and right after doing that they prompt you with a new message saying you already own it and. An install for free again. You could only be charged if the device is jailbroken, the Apple ID is not the same as the one used for the purchase or you were refunded.