We shake our puppy during tug-o-war. Also shake his head when playing get away from his teeth. Are we causing shaken baby syndrome?

Playing and shaking puppies is normal but be aware it's not long periods of shaking and it's not too hard. Also don't encourage rough play. Our puppy played very rough and we didn't correct the behavior and later on she got too rough and it was harder to correct the behavior. If your pup starts playing rough just gently lay him on his side until he calms down and gives up. It's what the mama dogs do and teaches submission. Also making loud yelps if he bites too hard will teach him how to control his bite while playing. We also had to teach our puppy this once she got bigger bc we didn't do it from the start.

I doubt it. Have you ever saw a dog catch and kill another animal? (squirrel, rabbit or bird for example) THEY shake the heck out of their prey! It's natural for THEM to do this. With that said, don't abuse your dog, which I'm quite certain you are not doing.

Edit: Hold on a minute...you shake the WHOLE puppy? Hmmmm, I guess I'd actually have to see what you are doing before I could make any judgment.

Depends on how hard you play, dogs are aggressive that they probably can't get "shaken baby symdrome" I'm afraid to play dogs like that because I'm afraid I'm hurting them if I play tug-o-war with my dog.

It's possible. Hard shaking is known to cause brain damage and not just in humans.