yes its a military one.
Think of a chess game as a war. Your strategy may be to attack on the left, the right, or in the center. In that case your strategy is your military (chess) plan of action. Suppose your strategy is to attack the enemy king wherever it is. Your pieces are placed strategically if they are helping in the attack. If they are not helping in the attack then they are not placed strategically.

What you all seem to be forgetting is that the English Language (and therefore it's dictionaries) are directed by useage, rather than vice-versa... the dictionaries are the ones catching up with those speaking the language. Therefore, us using the word strategically in a non-military sense is more correct than what the dictionary tells us.