Each player has skills such as balance, momentum, and grip. When the player is running, have a deck made of obstacles that can be overcome in different ways, such as running around, going over, etc.
The core mechanic is this: The player has to keep track of the last X skill checks, X being momentum (so it starts off at say, 7, and lower is better). If they get Y failures in that time (Y = Balance), then they stumble, and fall back a certain distance. Whenever they try to do something (shimmy up a pipe, jump a gap) they have to make a skill check (against grip, slide, hacking, whatever).
Each player keeps track of a distance while they are running. Choosing to make a skill check off of an obstacle (like climbing over a fence rather than running around) risks you losing your balance, but if you succeed you get an extra distance jump, and stay ahead of the pack.
So if someone has a good grip, they would be likely to vault fences, but not as likely to tackle locked doors. The enemy (or whatever the motivator for speed is) travels at a constant rate every turn, and anyone who loses their balance or is too slow is in serious danger of having to fight them. Police, for example, could be fought off with hand to hand, but helicopters would take something more. Maybe they are shot at every turn until they get ahead of the enemy again.
This would be more of a competitive game, but you could have co-op as well. A player could slow down and assist a teammate, giving them a big bonus on a skill check, at the cost of slowing themselves down.