Quant, that is not how most folks in the hiring/talent/HR business define people skills.
There is a large and growing body of literature about “people skills” and the extroverted, sales type personality that you describe is a pretty small piece of it.
And “social success” is often not even included. There is ABUNDANT evidence that serial killers for example- often present with enormous social success. Part of the pathology is their ability to be everyone’s best friend. The popular view of a sociopath is someone sitting alone in a cabin in the woods plotting the downfall of civilization- that does not jive with the statistics on sociopaths who have been convicted of violent crimes, many of whom have led lives as “the life of the party”.
There are many successful professionals with terrific people skills who are quite introverted.