I mean, you have to nail down the definition of think.
Neural networks are attempts at programmatically mimicking the way the brain works. Because of how computers work, it obviously can't work exactly the same as the brain does.
The fact that they hallucinate and get stuff wrong isn't evidence that thinking isn't happening; people are confidently incorrect all the time.
It takes an input, processes it using the data generated by its training, and provides a unique response. That sounds like thinking to me.
But the technology is still basically in its alpha phase, and unfortunately idiot tech execs are selling it as a finished product.