I think you're misreading that sentence. The sentence you quoted is basically saying: "you can signing into your AirDroid account from a traditional PC and connect to your phone over your phone's mobile network, instead of having to be on the same WiFi network." You can't use AirDroid to access your phone from a traditional PC without signing in first, and then making the connect either via WiFi, or mobile network.
I could be mistaken though. I'm still relatively unfamiliar with a handful of the features of the app.
I could be mistaken though. I'm still relatively unfamiliar with a handful of the features of the app.