tl;dr it was commissioned, constructed, and closed due to local safety concerns in the wake of the Three Mile Island accident.
Interesting excerpt from the wiki:
In 2004, the Long Island Power Authority erected two 100-foot, 50 kW wind turbines at the Shoreham Energy Center site,[18] as part of a renewable-energy program.[19][20] At a ceremony, chairman Kessel stated, "We stand in the shadow of a modern-day Stonehenge, a multibillion-dollar monument to a failed energy policy, to formally commission the operation of a renewable energy technology that will harness the power of the wind for the benefit of Long Island's environment." The turbines generate 200 MWh per year, or 1/35,000th of the energy the nuclear plant would have produced.[21]