It really depends on your definition of statistics.
For example, quantum physics is pretty much statistics, but how those statistics are used give rise to the explanation of the physical world, because of the complex interaction patterns.
To say that GPT is generating the next likely word sounds simplistic on the surface. It makes it seem like the model resets itself after generating each token, just looking at information before. And when running the model, thats exactly what it does, but thats just the algorithm part. There is a lot more information in GPT then it seems, its just compressed.
Just like cellular automata, universal turing machines, or differential equations describing chaotic behavior, there is a concept of emergence of complex patterns from very simple rules. When GPT generates the next word, its effectively changing its internal state because that word is now in consideration for the next token. And this process repeats itself for consecutive words. But this process is deterministic, and repeatable (you can replace the random process of temperature parameter affecting word selection with a pseudorandom sequence generated by a formula and achieve the same effect)
So just like the autoencoder/decoder networks effectively compress images into much smaller arrays, GPT compresses not only textual information, but sequences of states. There is quite a bit more, a whole shitload more in fact, information in the GPT model than just statistical distribution of the next likely word. And if you were to decompress this information fully, it be roughly the equivalent of having and extremely large lookup table of every possible question and its responses that you could ask it.
So all it is is just a very effective, and quite impressive at that, search.
And its both significant and insignificant. Significant, because after all, AI is equivalent to compression. Philosophically speaking, the turning point would be the ability to compress a good portion of our known reality in a similar way, then ask it questions, to which it would generate answers that mankind was not able to answer, because mankind hasn't bothered to interpolate/develop on its knowledge tree in that area. However its also insignificant in the grand scheme of things. Imagine moving beyond lookup tables. For example, if I ask an AI a question "A man enters a bathroom, which stall does he choose?", an AI should be able to then ask me back specific questions that are needed for to answer the question. Go ahead and try to figure out the architecture data set for that task.