句子的主干为it is possible to play simply for the fun and exercise。
it 为形式主语,is为系动词,to play为真正主语,simply for the fun and exercise为play的目的状语。
on the village green为地点状语。
where引导定语从句,修饰the village green。where引导的定语从句中含两个并列的部分:Where you pick uo sides和where no feeling of local patriotism is involved.第二个where被省略了。
On the village green, (where you pick up sides and no feeling of local patriotism is involved), it is possible to play simply for the fun and exercise:
括号为地点状语 修饰 village green
原句的结构是这样的it is possible to play simply for the fun and exercise On the village green (where....)