The Hunt for Red October/Headscratchers

How did Ramius kill Putin?
We see him slam the Putin's head against the table and do something to him slightly off-screen that looks like it could be CPR chest compressions if he wasn't murdering him, then we get a shot of his wide-eyed, stricken (yet still alive) face, which makes it look like he can't breathe. So how did he die? This one has always had me slightly puzzled.
 * I always thought Ramius.
 * It was a broken neck - this is made clear in the novel.
 * Specifically:

So does Putin exist in the Ryanverse?
Does Vladimir Putin exist in the Ryanverse or did his expy get killed by Ramius?