Open the Store Select Your Apps.... filter by ones not installed on this computer, select the App and Install, or Search for the App and Click Install
When I filter by "not installed on this pc" it says "all of your available apps are installed on this computer".
I hope they don't want me to pay again.
What happens when you search for that App? Did you uninstall or unpin it from the Start screen?
You are using the same Microsoft Account? You can email their support with a copy of the Billing Confirmation Email that Microsoft sends with every purchase...