Q: I purchased and later deleted one app a few years ago. Why do I need to pay for the same app again if I need to reinstall it today?

About three or four years ago, I purchased this kid game app. Later I deleted it after a few month. Now I want to reinstall it on my device (the same machine that I downloaded the original app). Without changing my ID/password, I now see that there is price by the app in the App Store. Therefore, it seems that I need to pay again to get this app nowadays. Shouldn't it be only one time charge? Or, just too many years between deleting it and reinstalling it could be a factor?