The implication seems to be that the CEO is autistic and thus sensitive to eye contact etc.
This article discusses the "autistic coding" of that character:
In Adam McKay’s Don’t Look Up, Peter Isherwell (played by Mark
Rylance) is the genius founder of tech company BASH. He seems to be a
cross between a Steve Jobs and an Elon Musk, but with blatant autistic
coding. His character is first introduced at a sort of symposium
presentation and before he comes on stage, there is a voiceover that
“Before we introduce the founder and CEO of BASH, please remember to
avoid eye contact, sudden movements, coughing, or negative facial
There is rapturous applause. As he enters, Isherwell’s mannerisms are
stiff, his facial expression fixed in a sort of half smile, and when
he speaks, his voice is high pitched and tonally flat. When a child
tells him, “I love you, Peter,” he ignores her.
I’m not sure how anyone could make eye contact through the glare of
stage lights. The connotation around this bizarrely timed request for
accommodations is that they are strange, and they set Isherwell apart
That alone would be enough to signal to me that the filmmakers have
Isherwell as autistic coded, but it gets worse.