Would summarizing peer-reviewed articles on a blog count as academic participation? I was a former college instructor (as an adjunct), but ultimately left academia due to low pay. I have no intention of going back to academia any time soon (for a variety of personal and non-personal reasons). However, I am still interested in academia, and would sometimes write about interesting peer-reviewed papers on my own personal blog.

Would writing blog posts about current academic research be considered a form of participation within academia (without having to actually enter into the toxic and less-rewarding atmosphere of academia)? 

I understand that I am talking to a 'non-academic' audience (and that there is a difference between popular literature and academic literature), but I would also be helping promote academic literature while also providing critical commentary on it.

For the sake of this question, let's define "academic participation" as "the ability to call myself an academic".
In a comment, you clarify that by "count as academic participation", you mean "I could call myself an academic."

No, you could not call yourself an academic just because you write a blog about academic research. Or, rather, you can call yourself whatever you want but most people interpret the phrase "I am an academic" as meaning "I'm a member of the teaching and/or research staff at a university." Using the phrase to mean anything substantially different from that would be very misleading.