~snip~
Why would wait for another person to get infected before cancelling the games 
? The officials must cancel it right after they confirmed the case. The virus behaves rapidly and it can be passed from person to person and some without even showing early symptoms (because others are asymptomatic). How many people he interact with before finding out that he got the virus? You cannot trace it easily. What more if you let those people interact with new bunch of people. See? May lives are at stake thus they the best move would be an immediate quarantine. I don't think that they will stop the next games because of the infect people before. They already got the infected person who comes to that place, so that makes the sports staff will be careful in the next games. And if they found another suspected person who infects the virus, the sports staff can stop the games, and they need to reschedule the games, and if necessary, they need to stop for some time.
That is why, before people enter the place, the staff needs to scan and collecting personal identification from people so they know if something worst happens, they can handle it with fast.