Here's my entry, written over lunch while thinking about how much I enjoy Tsuro, which is kind of the opposite of this challenge.
BUMPER CAR DERBY
Theme: Four bumper cars going from the start to the end. Easy, right? Well they are bumper cars.
Goal: Make it 15 spaces on a board that is built with square tiles as you race. Each tile represents your path.
Mechanics
Draw until you have three tiles in your hand. The face of these tiles are hidden from view of the other players.
Lay one tile so that your token (bumper car) is moved along the path. Each tile has multiple paths and can be placed in any configuration. You must lay the tile so that one side lines up exactly to the tile next to it.
If the tile puts you on the path of another player's car, you have run into them and sent them spinning. Move their car onto a different path on their tile and then follow it to the end of that path. This is where they end up. Do the same for your car.
If any bumper car runs into another bumper car, you get to pick the paths the new cars end on until all cars stop moving at the end of a path.
If a car ends up back at the start line, they can place a new tile next to any existing tile at the start and try to catch up.
The first car over the finish line, after the track is 15 tiles long, they win.
Trade-offs
As long as the tiles are well designed, the players will weave and exchange positions, allowing someone who can follow all the existing paths to see the best way to get to the finish. As the track gets laid out, other paths will become available so that someone kicked back to the start can jump forward on existing tiles. Bumping someone off their current path should throw them back several tiles, or may put them in the way of another player, or may force them to place a tile sideways delaying their forward momentum.
Stupid bumper cars.
Each tile side should have 2-3 paths available with many ways to cross paths and a few, but not overwhelming number, of turns.