Where am I going wrong?
Tohei is right and wrong. Unfortunately, not even the best aikidoka are the best linguists.
There is only one reading reading of 気, and that's "ki". "Ke" and "ge" are simply dialectal differences. "Iki" as a reading is considered non-standard. And it's possible that "iki" is derived from "ki". 気 was sometimes used to write "iki" (breath) back when Japanese orthography was looser, and people would occasionally use a different kanji with a similar meaning as a way of adding nuance. Another example would be writing "oto" (sound) with the kanji for "koe" (voice), or even vice-versa.
What Tohei is totally wrong about is that "ki" is onyomi. There is no kunyomi for "ki", aside from the abovementioned non-standard but possibly related "iki".