There is bound to be a small amount of play, otherwise it wouldn't spin.
If you had snapped the pedal spindle, then it would be obvious if you
wiggled the threaded bit.
Chances are it's just a small amount of bearing play.
On some pedals, this is adjustable. Is there a removable cap on the
end of the pedal? Under this you may find a locknut. It's a while
since I did any pedal maintenance so I can't be clearer.
Pedals are a replaceable component anyway, if all else fails.
For goodness' sake, don't go crossing the thread when you refit the
pedal to the crank.
--
Mikefule
So, do you ride with a club?
No, but I carry a heavy spanner.
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