I'll be honest. I had trouble understanding one section of the clip (the majority of the first half), and of course the speech impediment is apparent.
(I have slight speech issues myself, but of a somewhat different nature and more minor, but similar slurring at times and people often misinterept me based on my pronunciation of certain letters, etc. I have to be focused on my vocalization in order to keep it intelligible.
May also have something to do with the fact that I rarely speak for extended periods of time and possess physical jaw/teeth/mouth issues.)
However you don't come across as unintelligent, you come across as self-aware and competent, just trying to get through the impediment.
I understand why it bothers you and how unfair it is to have others so easily judge and assess you based on something outside of your control.
Would speech therapy help at all in your case?
(If it's something that has become too much of a barrier.)