Between my phone and tablet I can get the same buzzerbeater experience I get on my laptop (including watching games using the Dolphin browser).
I have the site bookmarked in all three devices and Chrome autofills the login and password. No problems.
Yes zooming in to click on the menus on my phone is annoying but not a deal breaker to me.
Overall mobile user experience for me? 3 on my phone (dolphin doesn't work on it) and 5 on my tablet. Both are Android.
Would an app help? That depends on what exactly you want it to help with.
Making it easier to watch matches without using Dolphin/Puffin or some other browser?

Bringing in more new users?

Retaining those new users?

The basic problem is that the app would still direct people to a game that is a slow moving, long-term type game. Without changing the user experience the only thing an app might accomplish is turning over more new teams in to bots every 6 weeks.
Don't mistake these comments for not supporting developing an app. It is a good idea. However, lets be realistic with expectations from it. It's probably not the silver bullet to magically turn around the overall buzzerbeater experience.