From a chemistry point of view it makes no difference.

There are many types of polyethylene. This particular type used by Lego apparently can be recycled more easily than other types of polyethylene for reasons not explained in the post. As for why it matters whether the plant is living or dead, there is a vast order of magnitude difference in the energy extraction cost from living plants vs finding, drilling, refining, processing, and transporting dead plants. Oil extraction is expensive and the various processes required to extract and use it come with significant environmental externalities.

You can make polyethylene from air. Are we calling it atmo-plastic now?

Citation needed. As 1/3 of the most common polyethylene molecule is carbon, and 2/3 is hydrogen, you would need some very special air to make polyethylene.