Do CTOs code? John Carmack (CTO of Oculus, former Lead dev for Quake) implies he still writes software on his projects

Listened to this podcast with John Carmack and from what he said in the interview it appears that he still writes software on the projects he works on including Oculus:
https://www.youtube.com/watch?v=udlMSe5-zP8#t=1h24m50s

Is directly contributing to your organization's code base as CTO something that is standard in the tech industry, or is Carmack the exception rather than the rule?

TC: 90k
YOE: 2

Joe Rogan Experience #1342 - John Carmack YouTube