If the app is in your download queue then you won't see the button however if you have issues downloading it.
Cancel it from your download queue by tapping the hamburger button then downloads and updates.
Or Simply wait a few seconds for the store to load the download queue and click the down arrow next to the magnifying glass.
Close the store as sometimes it take awhile for it refresh and the download button should appear again.
However if it is fully downloaded then it may take sometime for "This product is installed" depending on your internet connection.
As you can see below from the image.