The online save function for participating Flash games seems interesting, but any time I open them it claims "it's quiet in here". All tabs (Today, This Week, All Time) show "0 total, 0 Average Score". I made an account to check and submitted a score to Nyan Cat Fly to test but it only shows up in the My Scores tab. It's also worth noting that the high scores dialogue only opens (for the two games in which I have tested them in, Checkpoint and Nyan Cat Fly) when I download the .swf and run it locally in my browser (With the native NPAPI Flash Plugin). It's entirely likely that it was shut down due to the majority of games being played on Ruffle now and perhaps the emulator didn't support the API and as such it was deactivated, but I'd still like to know definitively.
It should be functional, as it's just a component of our overall API which is still supported, and still works for things like storing save files and premium purposes.
Based on what you're describing, you're talking about leaderboards, not online saves. It's definitely possible that Ruffle emulation breaks some/most/all parts of the leaderboard functionality... but i know for sure that premium purchases work and online saves work (check Kingdom Rush, for example). It may be that special fixes were required on a game-by-game basis by the Ruffle team, meaning only the most popular games have had fixes.
Nyan Cat Fly, for example, does not even have saves, but it does have leaderboards.