Perhaps the creators translate it as kid = kölyök. Unless kid is accepted for gyerek elsewhere, it isn't a mistake, imo.
"Child" and "kid" are largely interchangeable in modern colloquial English. (At least, in North America -- I can't speak with certainty about UK usage.) The distinction is that "child" comes across as somewhat more formal than "kid". For purposes of this lesson, both "child" and "kid" should be accepted.
Is there a different form for playing (present continuous) and play (present simple) similarly to megeszik and eszik? And can that -meg be applied to any verb?