Yes, the keyboard does have a tactile feel to it. It is probably not damaged.
All of the XPS 15-9560 keyboard keys have a bit of play because they are raised above the keyboard cut outs. You can press the sides or corner of the keys. But it is better press the center of the key.
If it's not to your liking, or you feel yours is damaged you could troubleshoot with tech support and see if they would replace it.
You can contact Tech Support at 1-800-624-9896 or 1-800-288-4410, or you can initiate a chat session http://dell.to/2v4snVm