Mid-game is the period in a match where the strategy of the early game can come together, allowing for the first combat engagement(s). While a Dark Templar rush is 'early' it takes place in the mid-game because this is the moment at which the strategy comes together for the player that is rushing. It is possible that the player he is rushing is still in the early game, which may cause a lot of stress to be able to fight off the push. However, this accounts for any tactic. If you have all the units you want and feel ready to attack, you are effectively in your mid-game. Mid-game typically starts between 7 and 12 minutes, depending on the tactic used and the level of skill of the individual players. Mid-game pushes can end the game in a victory for the first player reaching it.
Choices in mid-game
While choices made in mid-game are not nearly as crucial as choices made in early game, they very much define the ongoing succes (still a chance at winning the match) of a player. Players who have executed their strategy by playing their early game economy to the fullest efficiency and start to mount a first attack with the units they have created are starting their mid-game, but that does not end the complexity. The complexity of a mid-game increases as micro in engagements between opposing players decides that the players are on equal footing and make them unable to take each other out with their early game strategy. At this moment, a good player starts working (or is already working) on his late-game strategies by expanding and preparing for new strategies while continuing the pressure or aggression if he has the APM to afford it.