There is no app to download from the App Store or Google Play. But you can still get the feeling that it is an app, and the speed that comes with it. A tap on the home screen and you get directly to your player profile page, where you can see upcoming matches and report results.
This description applies to Iphone iOS, but works similarly to, for example, Chrome on Android.
On the iPhone, you can only install it with the Safari browser. And in order for the experience to be good, you need to have upgraded to iOS 13.
Open Safari and go to go.league-systems.com (or whatever domain you're on). You don't need to log in if you haven't done that already.
Then click the Share button (a box with an up arrow), followed by Add to Home screen. Done!