You don’t have to install it through the Windows store and uninstall the old one, but that is one potential solution (and likely the easiest one). It’s up to you.
If you’re just asking if the above is the correct application to install from the Windows store: yes it is. After installation, you should be able to launch the IDLE via one of the above commands, such as python -m idlelib (I don’t remember off the top of my head which one the Windows store version uses, as I don’t regularly use Windows these days) or from pressing the windows key and searching “idle”. IIRC, installing it from the Windows store adds a specific launcher for IDLE.
Hopefully that helps. 