As with many chemicals the order of the atomic arrangement makes a difference to the properties.
See:
Isomer - Wikipedia
Where the exact same atoms are in each chemical but the arrangement makes a difference to what their properties are. They are however, still chemicals and only chemicals.
In the case of DNA the order is known to make a difference to the resulting chemistry when the chemical processes which create proteins occur. It is all still chemistry however.
Chemicals are not just the atoms as you seem to suggest with your thought experiment. They are also the order of the atoms. But this is still chemistry.
If you disagree I would like to sell you a gram of graphite for the really cheap price of, for you, $20,000 US.