Is the usage of “at play” limited to children’s action?

In play is the correct term here, as it refers to items that are currently in use in some process (and does not pertain to children in any specific way). "Once your hand is beaten, the cards are thrown out and are no longer in play".

I would also suggest that the issues "at hand" would flow off the tongue even better than "in play". At play, I believe is really pushing the boundaries of what that phrase means.

As I see it, at play here implies influencing/ controlling.

The issues at play are the factors that affect the decision or drive the outcome.

The word play has far too many different meanings beyond those mentioned by you.

As noted in etymonline's entry for the noun play, «Meaning "free or unimpeded movement" is from 1650s.» This meaning of play is seen in wiktionary's sense 9 of noun play, "The extent to which a part of a mechanism can move freely", but it also allows issues at play or issues in play to mean issues that are under discussion, with outcomes still to be determined.

The OED says that at play means “engaged in playing”, and that in play means either in jest (rarely) or today much more usually, some variant of actively engaged, occupied, or employed.

There is also to come (or call) into play.