You do need whatever device you’re using to manage the tournament to have access to the internet. Most people use their phone for that, so no problem.
From there, setting up scoreboards at each court takes your tournament to the next level, and they do need internet connectivity. Displaying a dashboard on a monitor, projector or TV can also make an event more fun, and that’s obviously got to have internet access too.
If you’re in a location without WiFi you can use a mobile hotspot, either your phone’s or a MiFi device. More on that here.