This sounds pretty accurate to me. I personally got into programming because I wanted to create a website to share my knowledge online, and then felt like adding more and more interesting features to differentiate it from the crowd. I also learnt a lot about it due to wanting to code games as well.

Wouldn't be surprised if something like 60-80% of programmers got started because they either wanted to make a website about something or they wanted to make a video game/video game mod. After all, nothing drives you to learn more than having a clear goal in mind and needing to find solutions for how to achieve it.