Play is not accepted in this case.
For it to work, we would have to be able to rephrase it as a simpler clause, thus:
*Jay made activities / Jay makes activities.
Jay did activities / Jay does activities.
*Jay played activities / Jay plays activities.
Syntactically they're all fine, but the first requires an object that makes sense with the meaning of make which suggests creation, so requires something he could "make". Activities would be strange here.
(It is perhaps in the list precisely because in some other languages there is a word that covers both this and also do, so some people with English as a second language will confuse them).
The third similarly requires an object that makes sense with play, and we would only allow this with certain nouns, such as games, musical instruments, tricks, or the names of specific cases of those.
Really, I'd say this is a worse choice than make.
I suspect this is simply a slip by the teacher.
I note that while I can't see the answers in the preview here, the phrasing of the question does definitely suggest one pick a single best answer. The implication is strong that there is one, and only one acceptable answer.