They smile with their colours and they also chirp or honk occasionality. And sometimes click. Or even purr. I've adopted their language to some extent under stress or overwhelm! Most species of day gecko change colour intensity under various stress conditions. Of course, this is useful because you can generally tell if they are OK or at least "coping". Whereas humans (or at least the English) basically lie most of the time.
Broadly speaking if they are bright green like that they are safe and happy.
It's funny that they do look like they smile, this is basically anthropomorphisation of babies smiling etc, because the way the jaw is constructed it turns down at the edges. Once you see that, you realise they're kind of smiling and frowning at the same time, giving them a cute sort of derpy appearance. Of course, they don't have any of these muscles we do, so it's silly. But for sure it's hard not to imagine them smiling when they are happy! I think when I was a child, I just saw this gecko in a book and thought, it was bright and green and happy looking, and very squishy and substantial compared to other lizards... Whereas I wore black school uniform, was underweight, and basically couldn't smile. It became my spirit animal.
The eyes appear glossy and responsive when happy and dull and unresponsive when sick. Which is a part of a smile we often neglect in humans too.