Also you have to remember that even if you are logged in you do not maintain an active connection to buzzerbeater. If you want real time, you have to spam the refresh button to get updates coming constantly.
Well, on this part I know for sure that your wrong.
The "live view" of the games are just that - "real-time" connection and update.
Hence, as I wrote, you can add another short information that an additional plug-in could read and use a sound that is part of that plug-in.
Again, another option is to have the game live-view recorded with sound at the server and send it as part of the live-view, or by downloading it.
One more thing;
As the live-view is... live (meaning, RT), and as sound is low rate data (especially the first step of calling score change).
And as I guess it is not higher that the data sent for displaying the page.
Due to all that, I believe that the cost here is very low.
Last thing;
As I wrote in another forum, neither of us is a developer of this site.
As such, we do not know exactly what can and cannot be done.
We do not know their priorities.
So, this forums here should only be about suggesting feature and discussing their need (this suggestion is only a "nice to have", as I wrote).
The effort and cost are for the developers to define.