I believe tourist visas are issued only for specific events, such as a Formula race. Fans (or maybe "fans" is more accurate!) can do other things while in the country. I guess you'll need to keep watching for something like that coming up.
In January 2018 I got a 5 year multiple entry business visa for Saudi Arabia. I am American. I used a visa agency. While very expensive, it was rather simple once I figured out what I needed to do.