I don't necessarily agree with the concept that leadership should truly only mean "leading people" or that you need to demonstrate leadership via "extracurricular activities."
One, "Thought leadership" is a perfectly valid idea to elaborate upon in your essays, and going by your definition of "leadership," it provides you with an opportunity to offer an alternative interpretation of what leadership experience might comprise.
Two, to give you another idea that I emphasized upon heavily in my essays, think about what else personal leadership could mean to you. I took it to mean to be the ability to step out of my cultural comfort zones and take initiative to be more involved in the world at-large around me, and hence in my essays I spoke a lot about living and working abroad, learning a new language in unfamiliar cultural surroundings and that seemed to compensate for my lack of traditional leadership experience.
Hope that helps.