Pls divide the situation first
Running in playground w/ others is gd sign and encouragable, it is the beginning of social interaction, I found there are a lot of kids running around and around, you should encourage yr kid to have more interaction w/ other kid after running or during running. Say like making it as a competition at a certain pt with other kid, or adding playing instrument after running etc. It also use up its energy. Pls do not discourage yr kid to run w/ others. It's should be a very encouragable thing. Do u prefer yr kid playing alone or concentrating on a specific instrument rather than running w/ others. Of course, the latter is better la. Social interaction is the ultimate goal rather than playing instrument in playground , right?
About running or chasing other people in public area, of course need remedy since it affects others, one possible solution is to normalize his behaviour and limit his action. If he has a particular people or area he run or chase, limit his running to a certain person (Of couse, most likely is dad or mom) or a particular area (say like a zebra crossing before the kindergarden). Everytime, if you pass this zebra crossing w/ him, saying that only u will run w/ him together. No other area, no other people. It is very important that it should be fun. Next time, if he runs w/ other or chase w/ others in other area, warn him that he will lose his chance to run w/ him in the crossing one time. Do carry the "punishment - not running" if necessary. After successful, cut such running behaviour by some other thing he likes (candy, play in playground, etc)
Hope it helps.