"Envision someone playing your game on a phone while developing" - Why? 

"All games must include a leaderboard system (offline or online) so that the players can compete for a high score if they happen to win the contest." - What does this mean? is it just a simple save file of your highest score in the game or something online (cus rip i can't netcode) 

yeah thats what i am asking myself too

The phone bit is because the jam hosts sometimes offer to publish successful titles on mobile. If that's something you're interested, it's beneficial to make a game that would play well on a phone.

My understanding is the high score can be as simple as displaying a number on the game over screen, or as complex as an online high score leaderboard.

You just need to display the score at the end of a run.