You forget a crucial fact: There is an influx of energy from sun.
The whole earth as an eco system works in a similar way as the plant and its environment in the experiment. There is no contradiction regarding energy. Law of Conservation of Energy applies as usual. From energy point of view, there is nothing to prevent the experiment from existing.
As for chemicals like water, plants return water to the environment to the great extent. It is actually amazing how much water evaporates from an adult large conifer during hot seasons - it is unbelievable. The similar logic can be applied to other chemicals. There may be off course a lot of complex chemical processes in such experiment. I guess after some time, perhaps 5 or 7 or 12 years, the system reached equilibrium, adjusting itself to the environment, and continued to function for so long.
Many factors can contribute to the outcome of the experient. But I think there is no proof that such experiment must fail.