Actual video of the event where Russian and US Navy ships almost collide. It seems that although not a legitimate game of "chicken" as they weren't approaching each other head on events like this could easily get out of control and have unintended consequences. It's never a good idea to be a bully in such a huge ocean with so much at stake. One wonders it this was a move by a single Russian Captain or a larger scale problem where someone much higher up in command has issued commands to challenge an adversary's ships?
The Russians have reported that the aggression was on the part of the US Ship however the trails of the ship as seen from above along with the actual video from a US Sailor that is linked to above, demonstrates that the offense appears to clearly be on the part of the Russian ship as it is the one that steers into the wake of and then overtakes the US ship.