James Stavridis, the military official cited in this article, is noted as a retired NATO Supreme Allied Commander. While his view may be relevant to the discourse surrounding the ceasefire because of his previous status, he is by no means speaking on behalf of NATO in any sense, instead simply stating his opinion.
The larger claim that Trump is directly responsible for the Hezbollah-Israeli ceasefire deal is more complicated. This deal likely didn't come about based on a singular factor like the American election results. On the Israeli side, domestic political pressures as a result of the wars in Gaza and now Lebanon have put stress on leadership. Hezbollah has been greatly weakened by the conflict, and more than a million Lebanese refugees have been displaced because of the fighting.
https://theconversation.com/why-israel-and-hezbollah-reached-a-ceasefire-now-and-what-it-means-for-israel-lebanon-biden-and-trump-244700
This Newsweek article below provides input from several international security experts, the majority of whom agree that there is no evidence that Trump's win or his incoming administration played any meaningful role in the ceasefire.
https://www.newsweek.com/trump-behind-israel-hezbollah-ceasefire-deal-1994687
Therefore this claim is misleading, as it misrepresents critical information regarding the validity of the claim that the ceasefire agreement is a direct result of Trump's win. Regarding the actual claim of the article provided, it is more of an opinion than an argument that compiles adequate evidence.