‘Mimic’ as used in the passage means

I am always amazed when I hear people saying that sport creates goodwill among nations and that if only the common people of the world could meet one another at football or squash, they would have no inclination to meet on the battle field. Even if one didn’t know from concrete example (the 1936 Olympic games, for instance) that international sporting contests lead to orgies of hatred, one could deduce it from general principals.
Nearly all the sports practiced nowadays are competitive. You play to win, and the game has little meaning. Unless you do your utmost to win. On the village green, where you pick up sides and not feeling of local patriotism is involved, it is possible to play simple for fun of it and exercise, but as soon as the question of prestige arises, as soon as you feel that you and some larger unit will be disgraced if you lose, the most savage combative instincts are aroused. Anyone who has played even in a school football match knows this. At the international level, sport is frankly a mimic warfare. But the significant thing is not the behaviour of the players but the attitude of the spectators and behind the spectators are the nations who work themselves into furies over these absurd contests and seriously believe at any rate for short period that running, jumping and kicking a ball are tests of national virtue.
Even a leisurely game demanding grace rather than strength can cause much ill-will. Football, a game in which everyone gets hurt and every nation has its own style or play is far worse. Worst of all is boxing. One of the most horrible sights in the world is a fight between white and coloured boxers before a mixed audience