So, the rules for the speedrun says "Starting from level 1 (select Easy difficulty), beat level 15 of Mowin' Maniac". I want to ask then, there's no category for starting at medium or hard difficulty and reach level 15?

Not at the moment. The Medium and Hard difficulties drop you into levels 6 and 11 respectively, so getting to level 15 from there would probably be a lot faster than Easy.

However, if I do see interest in running those categories I could add them.