I like that with the meaning of the race shows a tradition and not only that but a way to show manufacturing teams its latest greatest e.g
In automotive racing we have many types of car manufacturers to have them sponsor the driver and to use their vehicle in the race.
Some magazines or media would list an event to be featured in there show many enthusiast would be interested to tweak and style their vehicle for the world to see. They would have an entrance fee because it was not just any street race but one that was set by the council or some royal blood.
Demolition derby this could of been done because of the amount of additional trash in the wreckage to turn it into something useful. So they would use their Frankenstein vehicle and ram into others, the skill of the driver and the build of the vehicle was equally important.
Hill climbing race was another to get to the peak of the top first to perhaps lets say to get to higher grounds away from a flood or the ground cracking open and to get to the top would reset this occurrence by forcing a powerful way of energy that pushed back the flood or absorbed the shock of the ground cracking etc.
Alpine/down hill this i can imagine going really well with the meks avoiding obstacles getting to the bottom before the avalanche or the very dangerous hot lava rushing down to get to the gate to travel out in a speedy escape!
Cross country skiing with rifle shooting to develop their battle skills under harsh condition as the blizzard occurred they would find that skiing was efficient especially with the use of poles in the snowy conditions and to test their aim at hitting targets.
Earning points for hitting the target and finishing the race so even if a racer wins but could lose because of missed targets.
Skeleton racing i just vision this with a g-suit with energy shield around the pilot !!!
Drone racing having your little drones flying past a circuit in the gardens of the sky city some of the wipper snappiest of kids are the toughest challengers since they have mastered their skills in the simulation room at such a young age.
Buffalo racing (Kambala) was between two pairs of buffaloes. In villages, there is also a ritualistic aspect, as farmers race their buffaloes to give thanks for protecting them from diseases.
Dog sled racing lets for a moment consider that the sled in em8er is a a construction device on a sled or wheels or something and the dogs were meks instead with linked connections on your screen there would be a button to press on time so that lets say in dog sled racing its 11 but for this we can say 4-6 meks per team for example.
The lead mek pilot at the front would dictate the direction but the power would be among the other mek pilots who would have to time their button pressing as it appears on the screen to use the boost and even jump etc.
Wingsuit racing the high risk of being eliminated is there since you are not in a mek suit and the g-suit would have specialised wings plus to be less detected in the air. With reinforced suit your aim is to get to the ground at the target landing point after landing deploy your mek this would sound the alarm you then race off with the required supplies you are faced with tsi-hu hunters tracking you down shooting you, race fast and stay alive the survivors need the supplies and are counting on you!!
Pocket bike racing was done for fun as an entertainment but i could see this as a pet race where the pets would carry the owner done on a funny circuit and pop up obstacles could surprise you its not the fastest of races but its probably quite fun and cute at the same time
Direction finding racing these combined the use of navigational skills with the use of a compass, map and a communication device such as a radio. These were used to taught in schools as a way to combine science, technology, and physical education.
The map will indicate the location of the start with a symbol and the location of the finish.
Somewhere within the region on the map, will have placed five low power radio transmitters. The locations of the transmitters are kept a secret from the racers and are not marked on the map.
Each transmitter emits a signal in code by identifiable to the racers. The transmitters automatically transmit one after another in a repeating cycle, attempt to locate as many as three, four, or all five of the transmitters in the region, and then head to the finish line in fastest time they can.
G-suit Racing lets imagine an anti-gravity field we are floating here weightless and have magnetic boots to attract or repel off surfaces. The area have some tunnels and some floating objects so you can repel off using your sort of mega man style boots and when you start to go abit too far off activate the boot to either repel or attract e.g left mouse button is to attract and right mouse button is to repel
The purpose was to test the g-suit in anti-gravity conditions and it became a tradition for pilots to compete in the course
Just spewing ideas but i think racing could be done on many things here mek, vehicles, pets, the pilot them self even the use of a grappler to get from 1 point to another without touching the ground you could call it the Tarzan race hmm and if you swing and hit into enemies they could be knocked down because of the pendulum effect.