In the abstraction of the game, this reflects the crew moving more slowly among fallen debris and such. And operating a partially crippled ship, with more effort and less efficiency. Some crew would also be drained to urgent duties. Overall, this means that the number of actions available decreases on a damaged ship.
True but this is due to some randomness in putting the chits in the boxes. In the example at page 29, the one relevant for action number, the hand and number is half covered by hull damage. Please imagine the whole box covered by the chit. This is the general intention.