alt Hacker NewsGraphcast (the model this is based on) has been validated in weather models for a while[1]. It uses transformers, much like LLMs. Transformers are really impressive at modeling a variety of things and have become very common throughout a lot of ML models, there's no reason to besmirch these methods as "integrating an LLM into a weather model"
A lot of shiny new "AI" features being shipped are language models being placed where they don't belong. It's reasonable to be skeptical here, not just because of the AI label, but especially for the troubled history of neural-network based ML methods for weather prediction.
Even before LLMs got big, a lot of machine learning research being published were models which underperformed SOTA (which was the case for weather modeling for a long time!) or models which are far far larger than they need to be (e.g. this [1] Nature paper using 'deep learning' for aftershock prediction being bested by this [2] Nature paper using one neuron.
[1] https://www.nature.com/articles/s41586-018-0438-y
[2] https://www.nature.com/articles/s41586-019-1582-8