So I actually put some research into this. The conclusion that I reached is that the cop tried using a police maneuver where you hook one of the subject's arms and wrap the other around their torso, taking them down. At first that sounded like a 'cover-my-ass' kind of thing, but then I thought about the actual logistics of it. Eric Garner is like a foot taller than the cop. It'd be near impossible to hook an arm and press downwards on their torso to bring them down, especially with a man of more portly size such as Mr. Garner. Imagine trying to grab the chest of someone a foot taller than you from behind, you would easily end up against their neck when you pulled towards you.
Then there's where the truth kicks in: what happens once the chokehold is applied. The chokehold is released when Mr. Garner hit the ground, before he begins saying "I can't breathe." This one is actually verifiable purely by the fact that Mr. Garner was able to actually talk and say "I can't breathe." Try having one of your friends strangle you while you try to talk. Tell me if it comes out anywhere near as close to normal as it did in the video. I'll actually save you the effort: your voice will squeak out in an extremely raspy and quiet tone. What actually happened was that the choking triggered Mr. Garner's asthma, which then prevented him from being able to breathe.
So the issue then becomes: was the chokehold itself excessive force based on how the average person would react to it?
Chokeholds are banned in the NYPD. They shouldn't be used. Assuming the officer had attempted to execute the move he said he was, but merely failed to properly execute it but released the choke hold as soon as was safe, the officer would be culpable for nothing. However, assuming the officer went in for a chokehold and later lied about it, the officer is culpable for use of excessive force.
So, once again, the issue changes: was the officer intentionally using a chokehold? I don't know if that question is possible to answer by anyone but the officer himself. What we do know is that he did not intend to kill the man, as he released the chokehold as soon as possible. With this information in mind, I can understand why he was not indicted. I don't know if I agree with that decision, but I do know that the trial would be a stalemate. In that scenario, the police officer would be the defendant. That means it's the job of the prosecution to prove that he executed the move intentionally, which is impossible.