OK, so hear me out. The Saudi king is the Custodian of the Two Holy Mosques. Since the Hajj is now becoming dangerous for the faithful because of climate change, that means that the Saudi king needs to act to protect the Hajj and the Two Holy Mosques. I.e., the Saudi king has a religious responsibility to act on climate change, by clamping down on CO2 emissions and curtailing hydrocarbons extraction. It's the will of Allah, man.
At least in what they say they certainly recognize this. The middle East as a whole talks about climate change much more than the US in my experience, mostly because to them it is an actual existential threat. Money is money so I'm sure they'll keep extracting oil while it makes money, but every single middle Eastern economy's goal has been to diversify from oil for many decades now.