Emulators are not banned by Speedrun.com, prime example being Super Mario 64. Thing is a question like this needs to be asked to the community directly because the communities are the ones that decide about emulator usage. That being said, this is a Flash game so there's not really going to be an "emulated version", but you really should be talking with the Papa's community about these questions you have.
i speedrun another webgame found on crazygames, and no, they are not emulators. hope this helped :)
Since flash is gone the most reliable way to speedrun flash games is to download the .swf and play it in the standalone flash player.
What is hosted online these days are usually "Ruffle", which is a flash player which does not yet emulate flash perfectly, a lot of games will break (most will work just fine and are allowed, but ask the community first and if you see obvious ruffle related bugs then stop running it on ruffle). Or worse, the game is ported to html5 which often becomes a seperate category due to all the differences.
I recommend just finding the .swf file somewhere, but probably your run is fine.