I had no idea extensions like Ruffle even existed, so I did some Googling, and came across this Reddit thread that discusses ways to enable Flash. One comment mentions they can't send game scores with Ruffle though.
(It also links to a Neopian Times question which shows it is allowed to use these kinds of things to play games/send scores, which is something I wasn't entirely sure of, to be honest.)
Personally, I wouldn't recommend using anything Flash related anymore though, as you're definitely opening your computer up to vulnerabilities. So... use any of the things mentioned in that post at your own risk, I guess.