Is it OK for a child's bike to have a radially-laced rear wheel? I was looking at the Early Rirder Belter 16" child's bike and noticed that the rear wheel has radial spokes on both sides.

In wheels built for adult bikes this is considered bad practice. From Sheldon Brown's site:-


  Wheels with hub brakes and drive wheels should never be radially
  spoked. Due to the near-perpendicular angle of the spoke to the hub's
  tangent, any torque applied at the hub of a radial-spoked wheel will
  result in a very great increase in spoke tension, almost certainly
  causing hub or spoke failure.


These bikes seem to be popular and get good reviews, so it seems that this isn't an issue in practice. Is this because of the small wheels and the fact that children don't produce so much torque?
For a kids bike where the rider weight is under 25 kilograms / 50 pounds a radial spoked wheel is fine.  

I've been trying to clean up and true an old 12" steel wheel with radial spokes and I'm truly astonished how strong it is.  The spokes themselves are identical to normal bike spokes, just the length that is different.  The cross sectional area is the same.

The rim is normally the same profile as a bigger wheel too, just with more curve on it.  This also contributes to the smaller wheel's overall strength.

I'd say a 16" would be fine, but a 20" and above should be properly laced.
If the rider is... over 25 kilos then perhaps a cheap wheel is inappropriate.
The rider will probably outgrow the bike frame in height before they get too heavy for it.