Don't worry about the slack - the car isn't running when you are checking it...
What you should inspect is damage to any of the links, etc.
You can check the tensioner, chain, etc all via methods outlined in the EM section of the FSM, depending on how far you wanna go:
http://www.nicoclub.com/FSM/240sx/91-94/EM.pdf
If it's been over 100,000 since the timing chain was last replaced, then obviously it's due for a replacement.
That being said, the slack looks normal to me. Remember that for KA24DE's, there is an upper & lower timing chain. It's the lower one is much tighter. The upper one has play when the engine is off.