A power user is someone who tries to leverage features of systems and/or software to more efficiently or effectively interact with the platform/service they are a user of far moreso than the average user. Because users of third party apps on Reddit are the extreme minority (just look at official app downloads VS TPAs), they're typically considered power users, as they are willing to go out of their way to make their experience better, even if it's just downloading and setting up their app.
Power users also tend to be more active users; if you use something more, you're more likely to want to improve the experience of using it. Someone who pays for extra features to leverage more power is probably someone who uses the platform/service a lot more than the average user.
They're called a power user because they're leveraging power by doing more to exploit (not a negative term here) potential out of what they have as a user; at least, that's how I interpret the phrase.