This is really not surprising in the slightest (ignoring instruction tuning), provided you take the view that LLMs are primarily navigating (linguistic) semantic space as they output responses. "Semantic space" in LLM-speak is pretty much exactly what Paul Meehl would call the "nomological network" of psychological concepts, and is also relevant to what Smedslund notes is pseudoempiricality in psychological concepts and research (i.e. that correlations among various psychological instruments and concepts must follow necessarily simply because these instruments and concepts are constructed from the semantics of everyday language, and so necessarily are constrained by those semantics as well).

I.e. the Five-Factor model of personality (being based on self-report, and not actual behaviour) is not a model of actual personality, but the correlation patterns in the language used to discuss things semantically related to "personality". It would be thus extremely surprising if LLM-output patterns (trained on people's discussions and thinking about personality) would not also result in learning similar correlational patterns (and thus similar patterns of responses when prompted with questions from personality inventories).

Also, a bit of a minor nit, but the use of "psychometric" and "psychometrics" in both the title and paper is IMO kind of wrong. Psychometrics is the study of test design and measurement generally, in psychology. The paper uses many terms like "psychometric battery", "psychometric self-report", and "psychometric profiles", but these terms are basically wrong, or at best highly unusual: the correct terms would be "self-report inventories", "psychological and psychiatric profiles", and etc., especially because a significant number of the measurement instruments they used in fact have pretty poor psychometric properties, as this term is usually used.