Roon has three pieces to its software architecture: Core (server), Renderer (playback), Client (controller). All three of these things can be one computer, like if you install everything on one computer and then just listen to speakers or headphones connected to your computer. Or all three things can be different pieces of hardware, like Core on a computer, Renderer as your Node 2i, and Client as the Roon app on your iPad.
The reason the Core needs to be on a computer is because it is a persistent server like a web server or mail server providing Roon service to anyone on the network. It still runs and does work if any of the Renderers or Clients are turned off. It doesn't need to be a powerful computer, unless you start turning on a bunch of extra processing stuff, but it does need to be always on.
Any of the Core, Renderer, and Client devices can be on Wi-Fi if supported by the device. Desktop and laptop computers, and phones/tablets, are all pretty much guaranteed to work over Wi-Fi, so that covers the Core and Client devices. But Renderers may not support Wi-Fi in which case you'll need to purchase a Wi-Fi extender.