Being rich means having the resources to influence the system in which you participate: having the means to shape the larger (social) organism you are a member of.

So what is valuable enough to shape the system? Outside of material means (currency), an individual may possess knowledge, skills to distribute that knowledge, and a perspective that informs both their method and opinion.

Put another way, you can have something you know, a way to share it, and a moral compass. These three tools, coveting and cultivating them, over time may allow you to influence the world around you by only being yourself, effectively making you "rich" in a way that does not require buying the means to change society.