A game is something played either alone or with friends that involves skill and or chance. Games also have rules.
So, for example, although you might play a video game on your own, you still have to play by the rules.
Some games are almost entirely chance. Snakes and ladders is like this. Others need a lot of skill. Video games tend to use more and more skill, especially in terms of quick reactions. Having to work hard at this level of skill may help to develop nerves that go between eye, hand and brain.
Many people, however, see a game as something played in the company of others. Chance games are mostly only worth while is played as a pastime with others. Board games like chess involve a lot of skill, while board games like Monopoly are a lot about chance (throwing the dice), but also about strategic decisions (which hotels etc to buy).