So when he says "250 gold to the first person to reach the rally point" then that's 100% fine (right?), but saying "250 gold to each person who doesn't go to the tournament" would violate the IR.
Correct.
In a similar vein, while attending a tournament is an IR, is holding a tournament an IR? That is, could the lord of a city be accosted for *holding* the tournament at a bad time?
No, it isn't, else it would be on the list. People who can hold tournaments can be assumed to be powerful and influencial enough to fight their battles.