Yes you do. The app is compatible with most Android phones and iPhones and is available in the stores to download for free. You already purchased the nightlight, so you don’t need to pay extra for the app! However the app is used to setup the device (make it connect to internet) and to setup the sleep times for your kid.
There are minimum requirements for the apps to be able to be installed on your phone. They are available in the Technical Specifications.