How can I repair cracks in a sports court?
You could patch up these cracks with an epoxy filler or a cement product type filler. In either case the filler will dry hard and be able to take the temperature extremes of your location. Repair such as this is going to leave tracks where the filled cracks were and will still be highly visible due to the surface texture that was originally applied to the slab surface. To get the best visual appearance you may want to subsequently consider prepping the surface and getting a new textured surface applied. Before doing that however please do read on to the next paragraphs.

These cracks readily show that the soil under the slab is changing position and settling. It also gives the appearance, due to the separation that has occurred, that the slab was built without any or a very limited amount of wire mesh and rebar installed. Both wire and re-bar cannot prevent cracks but will prevent large separations and variation of surface height across the cracks in most cases except the most extreme soil movement, settling, or water erosion under the slab. 

You will want to carefully evaluate conditions that led to the cracks in your slab. If there is continued soil movement any repairs that you do will be only temporary and could lead to disappointment and loss due to the cost of the repairs. In the worst cases it may very well be better in the long run to remove the sports equipment, break up the slab and remove it and the replace with a new slab that is installed in a way to prevent future cracks. This would of course include plenty of wire mesh and rebar. If the soil is unstable it may even be necessary to engineer a footing and/or deep peers that can stabilize your new slab.

If the cracks have been stable for a long time and you've seen no changes since the original incident then repairs with filler and a re-application of the textured surface may be a good longer term solution.