Quite a nice idea but it would need a few changes, because there's a problem I thought about:
Sometimes you become first because you're closer to the next checkpoint on a direct distance, while you're not actually closer, like when there's a U-Turn, or a highway exit (you know those exits that are like a spiral/almost circle).
And with the bad sync it's not the best thing either.
In my opinion it should be like overtake and keep the lead for some time... or better some distance (so it's not unfair between short and long races) like 5 or 10% of the total distance of the race.
But still this is a bit easier for the "defendant" who has to keep his lead. Maybe make it like the defendant wins only 50% of the stake if he wins, the challenger wins 100%? For example: I challenge Ush for 10.000$. He wins, he gets 5.000$ from me. He loses, I'll get 10.000$ from him.
(It also seems a bit logic for me that it's better the one who takes the initiative to challenge somebody is more "arrogant" so he'll have to do the harder job, and so people don't juste duel if they are gonna get an advantage toward the defendant)
Nice idea anyway.
Edit: oh and also I just thought, another problem is for the grid... what about one world races, or even normal world? Setting a new world for the players would be unfair toward others... Was your idea to make that completely out of /race (because I see [NEW MODE] so I guess it may be out of /race and some kind of /tt)