Yeah, how can the body tell which noble gas it's breathing? As the article mentions, the xenon is exhaled in its original form without having been metabolized or having caused any chemical changes in the body!
Different atoms have different sizes and if you look into how ion channels work you can see that there are many processes in biochemistry that are incredibly specific to size and charge
But it does cause chemical chsnges. Noble gasses can weakly interact. It does not need to form bonds to influence potential gradients, protein shapes, or other reactions.