Some people jokingly say that cats are autism and dogs are ADHD and if you know people who are autistic or have ADHD, the parallels are fairly obvious. Autistic people also struggle with other humans insisting on eye contact.
As do Finns (I'm one), and people of many other non-American cultures. And many non-autistic but shy or introverted or highly sensitive persons. You seek eye contact momentarily when you make a point in a conversation, or respond to a point made, or want to empathize, or whatever. Prolonged or too frequent eye contact is weird.
That said, cats very much do stare at your face when they want or are expecting something, usually food. They also have the adoring eyes-half-open stare mode you can see examples of at r/Catsmiring.
I would say that cats better fit the introvert archetype, and dogs the extrovert one, rather than something from the DSM. Anecdotally there's also a significant positive correlation with their respective owners' personalities.
