It's a rarer but well-attested form of the idiom "to pass the buck", which means "to refuse to take responsibility".
Prior answers went into detail about the etymology, so I'll ignore that and focus on the many uses of "the buck". In general, "the buck" means responsibility, particularly an unpleasant responsibility that you'd rather avoid. Refusing to take that responsibility, and handing the obligation to someone else, is "passing" the buck. This is a negative description; passing the buck is never or almost never considered a good thing.
As a noun, there are a couple different forms. "buck-passing" is a name for the general phenomenon; you might say that "Everyone in the State House has been inventing fascinating new forms of buck-passing this week", meaning that there was a problem or problems which no one in the state government wanted to take responsibility for, and many of them had spent the week vigorously trying to make it someone else's problem. If you want to describe a specific instance where someone passed the buck, that would be "a buck-passing" or "a passing of the buck", as in the excerpt you quoted above. For example, David Cameron, former PM of the UK, was not particularly known for buck-passing, but his political career ended with a passing of the buck on Brexit. He didn't want to deal with the conflict it created in his party and nation, and so he resigned and left the issue for his successor. This version is the one being used in your quote; "Trump's passing of the buck" means "a passing of the buck, which is Trump's".
The other main buck idiom is "the buck stops here", which means that someone is ultimately responsible for all decisions of some kind. 'Here' is not used in a literal sense; President Truman had a nameplate in the Oval Office which said "The Buck Stops Here", but here meant "with him", not "in the Oval Office", i.e. anything the US government did was ultimately his responsibility (wherever he happened to be at that moment).
It can also be substituted with 'there', or any figurative location. For example, if you worked for a tech company which took security seriously, you might say "for network architecture, the buck stops with the Chief Security Officer", meaning that even the CEO was forbidden from overruling them. It can even be a literal location used figuratively; Americans might say "the buck stops at the White House" to mean the same thing as Truman said. (Though as the news excerpt you quoted implies, that doesn't seem to be true at the moment.)