Basically, the theory of punctuated equilibrium is that species evolve in stops and starts, short bursts punctuating long periods of equilibrium. First, evolution still occurs by natural selection; the varying rate of evolutionary change is the matter of contention, not the process of natural selection itself. Second, the short bursts of evolution are to be interpreted by evolutionary time, where short might mean 100,000 years or more. Third, punctuated equilibrium sets itself up against a straw man, and can only offer insight to those who hold onto the naive theory that evolutionary change is constant.
The notion that evolutionary change is not constant is already implicit in the standard model; any evolutionary biologist worth his salt should be aware of evolutionary strategies, which in mathematical models can arrive at an equilibrium i.e. evolutionary stable strategy (ESS). A true ESS may never occur outside of idealised world of mathematics, but ecosystems will sometimes reach a close approximation, thus preserving the species who form it from much evolutionary change.
If such an approximised ESS did exist, we would expect any successful mutation, newly introduced species, climate change etc. to have a consequences on the whole ecosystem, spurring the rapid evolution of new characteristics to solve the adaptive problems posed by changing circumstances. Then, after some of rapid evolutionary change, in response to fluctuating selection pressures, a new ESS will eventually be arrived at, and will remain approximately stable until the next time.
This is only scratching the surface if we wish to explain how evolution occurs at varying rates, and none of it is inconsistent with punctuated equilibrium. Gould's theory seems altogether redundant, good only for rebutting a straw man. That would be entirely consistent with other straw men Gould liked to criticise, while dressing such criticism in impressive verbiage. I think Dawkins' recognised this, and has little time for punctuated equilibrium, or its popular portrayal.