Pretty much like you said. You manage the spaceship and the crew by moving the crew members from room to room. The exclamation mark icons in the picture represent tasks that can be done. In this example there is broken hull in three parts of the ship and the red icon tells that torpedoes can be shot. The crew members always start working on the tasks automatically when they arrive in the room. However, each crew member is unique and has a special skill set. The captain can take care of any task but the others can deal with only one specific task. Weapons officer can shoot torpedoes, medic can treat the wounded etc. Tasks are completed faster if there are several crew members in the room at once.
The game situation in the picture is quite difficult. The hull has only 3 hit points left, there is hostile spaceship shooting at us, all crew members are tired, 2 of them are wounded, and one of them is sick. Two crew members are in torpedo room loading and shooting torpedoes, but what should the rest of them do and in what order:
- Should they go to the Crew Quarters to rest?
- Should the sick captain go to the Medbay to be treated?
- Should they start repairing the hull?
- Should they go to the torpedo room to help others to load and shoot faster?
These kind of decisions form the core gameplay.
Then yes, your design is indeed good and if you trow some nice upgrades it will surely be a very addictive game