Both "play" and "playing" is correct here. People often see him (who is) playing basketball on the playground at the weekend. People often see him (who) play basketball on the playground at the weekend.

Understanding the Context

So essentially both carry the same meaning. You're presenting the participial phrase as a parenthetical, and probably supplemental, modifier. The question is how to explain why it fails as a direct modifier. It fails because personal pronouns, especially in the subjective case, don't typically work that way.

Key Insights

Things like "tall she" and "she playing the piano" aren't coherent phrases. I was playing hockey. You could use it as a way to say "No" when invited to play a game or a match or something similar. For example: Want to play a game of chess? I just played.

Final Thoughts

Give me an hour to recharge my brain. If you say, "I was just playing" it means that you were just kidding around about whatever the topic of the conversation is. For ... Is it idiomatic to say "I just played" or "I was just playing" in ... Played myself in scrabble. I won!

What is the difference between playing with someone and playing someone? What if someone is replaced with the speaker themselves? Is the sentence in the quote cor... meaning - What difference is between playing with someone and playing ...