Which Greek city-state was strictly focused on military goals and objectives rather than creating a democratic form of government?

That was Sparta.

Explanation:

It was famous for it's Agoge. It was a school for young boys that were separated from their mothers, and then they would live through harshest conditions, like living in the wild and fighting wild animals for food. When they got older, after more rigorous military training, they would go into war. They honored man fallen in battle.