Strictly philosophically, Zen is Buddhism school. And, in the article that you quoted, Mr Putin visited Shaolin, a Zen Buddhism temple.
You refer to these
https://www.businessinsider.com/sergei-pugachev-says-putin-not-evil-2014-11
https://www.theguardian.com/world/2015/jul/28/sergei-pugachev-putins-banker-interview-lives-in-fear
for a claim that Mr Putin doesn't strategize?
In both articles, impulsivness is implied on Mr Putin's side; but, Zen Buddihsm neither implies lack of planning nor impulsivness.
I assess that Mr Putin does strategize but due to different mindsets and cultures, Western people and foes (for obvious reasons) do not comprehend his actions properly.
But, perhaps, you may be right.