This is indeed vortex shedding and a pretty cool demonstration of it in action. In a nutshell, as the air flows around the lamp post the flow separates alternately from each side. Each time a vortex is shed the load on the post changes, and due to the design of the post, the elastic properties of the material, the weight of the light etc, there will be a certain frequency at which the oscillatory shedding of the vortices will match the resonant frequency of the lamp post and this can become destructive as the forces involved can be quite large. This is why chimneys often have those spiral runners around the top, these are designed to shed the vortices in a predictable manner, instead of the oscillating vortices shed by a pure cylinder and so stop the chimney from shaking itself apart. Similar to the bridge at Takoma Narrows bridge, when the wind caused it to break apart or when the Millenium Bridge first opened and the movement of people caused it to sway.
The cool thing about vortex shedding is that any cylinder will shed vortices in this way, from a very thin wire that 'sings in the wind' where the shedding frequency is so high it produces an audible pressure wave through to huge vortices that form around entire islands. You can predict the frequency of the vortex shedding if you know the speed of the flow around the object and it's size using the Strouhal Number which is more or less constant for an object like a cylinder.
Wrote a paper about using this phenomenon to scale data generated during CFD simulations last year and this kind of topic is right up my street. Knew one day my PhD would come in handy.