A game of strategy is a game where we influence the outcome through interaction with the environmnet mainly people. If played with a pseudo artificial intelligence it sometimes comes near the games of skill.
Its benefit is the open interaction in with other people. The game partners have similar starting points and evaluate how others humans may react under same conditions. So game strategys evolve with more or less spirit involved to get advanteges and/or protect artfully.
Board games like
Checkers
Go
Nine Men's Morris (Mills)
Mastermind