(BTW, inspired by fun things like "fishing in Ferrel" which would make an excellent competition by the way).
The game of "Tag"
Probably called other things in other countries - the game where you chase around and try to touch someone when you're "it". If you "tag" someone then they become "it".
This could be scripted so that NPC children would play it amongst them selves, but if they see a PC then they try to "tag" him/her. The PC is then "it". The PC can only make one of the NPC children "it" if they chase them and say "you're it" when in touching-range. If the PC fails to play the game, then the NPC children jeer and make fun of the "stinky PC". LOL. What fun!
Here are some other suggestions:
Ball games,
Hide and seek,
Eye-spy (guessing game)
On a more grown-up nature:
Card games (I know there are some gambling card games)
Chess
More fishing

and of course gnome cricket! (oh I wish)
They would all add a little life to the world, and give opportunities for non-combat-based RP.
Anyone else got any other nice suggestions?