The closest things I could find are Generalized Anxiety Disorder, Adjustment Disorder, Acute Stress Disorder, and Social Anxiety Disorder. But none of those quite fit the description given in the article.

There are numerous medical and mental-health conditions that become worse as a result of stress, but they're usually described more specifically, not as a stress intolerance disorder.

I would be interested in a company's ADA compliance obligations for someone who says they have a stress intolerance disorder. Is it reasonable to expect a business to alleviate anything that employee perceives as stressful?

Certain societal groups are particularly receptive to their bullshit (hint; us) and tear you to pieces if you try to tell them their "disease" is made up. It's easier to have a label for your poor psychological habits than to do the work to change yourself.