This is very frustrating and the type of behavior that makes it seem like Apple isn't interested in the open web or feature parity for those of us not on Apple devices.
In the mean time, I was able to write some custom CSS that I installed on my browser (I use the Custom Style Script add-on) to hide all the scores I could find. There might be one or two I missed, but this covers most of the screens:
Site: https://tv.apple.com
.epic-stage-metadata-title__score,
.lockup-overlay__sports-score__score__team,
.product-header--sport-event__scoreboard__score {
display: none !important;
}
I hope this helps a few of you until Apple fixes this for those of us watching in a browser.