Yes, You need the app to do the initial setup. The app is used for pretty much everything from configuring devices to the the Homey Pro to creating automation flows. Though after setup you may use the Web app at my.homey.app.
Setting up and configuring everything is cloud based. Your configured automations the runs local, unless you have cloud based related devices.
Setting up instructions are here
There is also a related discussion ongoing Internet is down, cannot access Homey?!
