Check out Spongebob Squarepants: Battle for Bikini Bottom category rules.

www.speedrun.com/bfbb

Any%: Runs performed on emulators or without linked video proof (with sound) will be rejected if faster than 1:25:00.

Yes it is the mod's job. I'm fairly new to this community so I have no idea.
Should I ask for mod?

Different leaderboards are managed by different moderators. I myself as a moderator require proof before I verify anything, and even then I watch the material thoroughly to make sure it's not TAS or anything, and that nothing against the rules was done. Some other moderators aren't quite this strict. With this issue, I'd recommend contacting the moderators of the leaderboard, specifically the mod who verified the run you're talking about.

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