How do i change the order that the platforms are listed on a leaderboard?

You can't. They are always listed in alphabetical order. (Which can be annoying if "PC" or "Web" are your main platforms)

It's not alphabetical, or anything logical. It's not entirely random either though, it's just a weird, probably goes by internal ID or something.

They're most likely ordered the same way they got added to the site.

I do think the option to change the placements of platforms should be possible since I'm sure multiple games have rarely used platforms as their first option.

It would be nice to change the default platform. With the most common platform in the default, mods have less incorrect submissions to fix.