Yes – the term ‘living’ would normally be reserved for trees, mammals and bacteria etc.. However; all of these are made up of atoms – same as the rest of the universe. Then there are the issues relating to the incredible complexity of the universe – that stars are born and die – and planets have regular orbits etc.. All that may not properly fit the definition of ‘living’ – but I believe it aligns very closely with what we understand as earthly living systems.
More to the point; if the Dorchester Pot is really 593 million years old then that is pre-Cambrian Explosion – when life on earth had not evolved past simple single cell organisms. And certainly there were not people around 300 million years ago that might have manufactured the artefacts that were found in coal. So how do we explain their existence.
The thesis that these artefacts were the result of some form of gene expression from remote places in our universe is of course only speculation. However; it is consistent with what we know about living systems – and given the obvious lack of any rational alternative I think it is a reasonable argument to put.