I'm having to think back a loooooong time about this, but yes, I might have used "play" with it. Remember that, especially when answering a question, we frequently don't use complete sentences!
Helen: What shall we play/do next?
John: French skipping!
Mum: What were you two doing in the back garden?
Kids: French skipping!
The kids' answer is a shortened form of "We were playing/doing French skipping".
So, in answer to your original question, if someone asked me what the kids in the photo were doing, I'd just say "French skipping" (or "Chinese jump rope" if that's what you call it). As a standalone sentence, I have no preference between "The kids in the photo are French skipping", "The kids in the photo are playing French skipping" and "The kids in the photo are doing French skipping".