Geez, I'm glad you're not war minister. It's a Chinese registered ship with a Russian captain.
If a terrorist crashes a truck with Portuguese plates into the US embassy in Berlin, would that mean Portugal's declared war against the USA?
But there is a "but", which is that in the articles of war, the flag of a ship does have quite a few implications. E.g. when two nations are at war, stopping ships flagged as belonging to the opposition gives certain rights of stopping and searching them, blockading their passage, seizing the vessels and cargo, etc.
And the relevant characteristic in that case is the flag, not the captain's nationality: > Art. 51. Enemy character. The enemy or neutral character of a vessel is determined by the flag which it is entitled to fly.
Of course this isn't really automatic and triggered by the smallest thing, both sides kind of have to "agree" to be at war, e.g. by a counter-attack, a declaration following the attack or something like that. And nobody really wants to take that bait, due to the huge consequences involved.
Yet, it is China playing with fire here, we all can be happy that none of the affected nations took them up on their "offer" of war.
They can later claim that the crew and captain acted on their own will, without orders from the Chinese leadership. They can duly punish the captain and crew or disavow the vessel and declare them renegade, disallow them to fly their flag. But without such a declaration, a nation such as China is responsible for the conduct of their fleets, be they civilian or military. And any vessel they allow to fly their flag is part of their (in this case civilian) fleet.