It would be play, as the sentence would read for example, 'Do you play different sports?',
'Pintsinker has played many different sports in his lifetime', or even 'Pintsinker is hopeless at playing different sports'.
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You say good at sports because you cannot be in a sport. You can be involved in a sport but not good in sports!
There are a great many sports that are played in the world. These sports include football, soccer, swimming, tennis, and Basketball.