I think compared to the majority of other owners, Jerry comes off as extremely insecure and somewhat backwards.
Most of these guys didn't purchase an NFL football team as a means of making a living, they were already huge successes, most of them owners of well known companies. This was almost a side interest to them. As far as the football operations, the majority doesn't want anything to do with that. Their only participation is when they hire/fire a GM. They are mostly in the background and most of the time you only really see them when their team wins the Super Bowl.
I think they first saw Jerry as a nuisance when Jerry would try something new in the marketing process. However, they later determined that Jerry is a great salesman who comes up with more ways to make money. I think Jerry's entry into the Hall of Fame was their way of thanking Jerry for the increase in revenue.
I think Jerry amuses them with his desire to be seen as an actual NFL football authority. Sometimes I think they deliberately appeal to his vanity so their team's management can take advantage of him sometimes.