My whole family runs (including sub 3h marathons) and not a single one of them writes online about running.
As far as I can tell they are not self-important, they just run. I also run, and compared to the rest of the family even more under the radar: I do no contests ever, I run alone, I run at night. If I ever speak to someone about it, it is because they asked or because it was the topic of the conversation before I entered it. Running is my thing that I do for myself, the rest doesn't give me anything. It is a good habit, a free time and helps me to release stress (which is mostly mental in my job).
So maybe your question could be rephrased: "Why are the posts I read from people who post online about running so obnoxiously self-important about it?"
As I don't believe runners are any more annoying than e.g. ice skaters I could think of one rhing. Like with noises the things we find annoying might also have to do with ourselves. A friend of mine is constantly complaining about how "obnoxiously self-important" vegans are. He loves meat, but as a somewhat rational person he knows he is wrong. When I ask him where those vegans are and what they do he can't point to any specific thing. You could sit a vegan on the same table as him and even if the vegan says nothing and minds their own business he would feel they are "self-important" — all while he would be the guy to start speaking about it.
I am not implying that a similar mechanism is at play in your case at all, I don't know you. But it is something to be aware of. If you e.g. are someone who feels they should run more, but never get around to it for one reason or another, that might color your perception of people who do write about it.