Marm suggested I write to the folks at the site to get an answer to my question, so I did.
Within less than 24 hours, they sent me a delightful reply -- I thought it was really nice of them to directly explain everything to me, and it means they're willing to talk about their type theory if you have questions.
Here is what they had to say about the 7 "double" types (e.g., "power-power").
So basically what we have here is similar to the prim-tert loop in MBTI, maybe -- instead of balancing our type with a secondary, we reinforce the primary somehow and "double down" essentially when we should be flexing and looking for another way around.
I suspect they've gotten this question before, since they sent me a PDF. I'll try to upload a JPG of it later.
Anyway, there are 42 distinct "regular" types, + the 7 "double trouble" categories that define someone via their primary at a stress point.
EDIT: Note that I'm not sure if I agree with them -- I don't know if I really go all "Anarchy" on things when I'm stressed, for example -- but anyway that's their take on it.
EDIT: Here's the image.
Jeez -- pure Prestige sounds like me in middle school.
Maybe these apply better to what we'd usually describe as "unhealthy" people of each type.
Perhaps this is obvious to many (it seems like it's obvious to @Marmotini at least), but this is specifically aimed at looking at how you naturally trigger fascination in others. This is something that has become extremely important to me due to recent events(some of you know why). So it seems quite independent of MBTI and enneagram, which are are extremely focused on internal processes. There are many, many systems for analyzing people, and they don't all map onto each other (no matter how much Ti might want to unify things).
Accept the past. Live for the present. Look forward to the future. Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of  data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield
The Deadbolt under stress rings true for me and is a particular blind spot. It took me many years to understand how I could still be acting like a bitch to others when all channels of connection with them have been shut down (exaaaaactly...).
4w5 6w7 1w2 sx/sp ⏩ ISFP
RLOAX (don't do it) ⏩ Melancholic Hufflepuff
A lonely island where only what is permitted to move moves, becomes an ideal. Jung
YOU ARE THE BULLSEYE. YOU SYSTEMATICALLY PRODUCE SOLUTIONS TO COMPLEX PROBLEMS, BUT ARE RESISTANT TO SHARING YOUR KNOWLEDGE.
You have exceptional attention to detail.
You rarely share your thought process or motives.
You analyze data and collect facts before acting, to ensure a higher-quality result.
You are competitive by nature and rarely come out behind.
You keep your emotions and feelings private, only sharing with a select few.
Sounds pretty accurate, actually.
Music creates order out of chaos: for rhythm imposes unanimity upon the divergent, melody imposes continuity upon the disjointed, and harmony imposes compatibility upon the incongruous. - Yehudi Menuhin
YOU ARE THE SECRET WEAPON. YOU SYSTEMATICALLY PRODUCE CLEVER SOLUTIONS TO COMPLEX PROBLEMS, BUT ARE SLOW TO SHARE YOUR KNOWLEDGE.
You prefer working independently.
You are innovative and solve problems unconventionally.
You remain calm in times of pressure, yet always pursue solutions.
You embrace new challenges that serve your goals.
You keep your emotions and feelings restrained but have a complex and rapid internal dialogue.
It's interesting...had my so do the test the other day, confirming what I already knew:
He had my secondary as his primary ( Mystique - perhaps I even learned it from him) and his secondary was Power, which I totally suck at and find completely fascinating. Meanwhile his dormant trigger is Passion - my primary and my dormant is trust, which he is reasonable at. He's no good at rebellion, but I know he really likes goofy, out of the box ideas (and I scored equally on Rebellion and Mystique)
As I looked over the other triggers, I found that aside from my dormant, I am indeed very much fascinated by the triggers I myself don't use that much, with the exception pf Mystique which we share.
Would there be some kind of 'familiar ground'+'complementary ground' thing in that?