If a man told you he worked with computers, it'd be odd to raise an eyebrow and respond "Are you some kind of computer boy?". The technician treated this woman's work as something special because she was a woman. In other words: A man that works with a computer is still just a man. A woman that works with a computer must be something special, a computer girl.
And bonus points for calling her a girl, which is just a little bit more infantilizing.
could be referring to "mad men" era secretaries as ibm era computers were just better fancier word processors/typewriters
edit: or maybe like IT helpdesk staff who are like janitors (i.e. they don't see a difference between calling environmental services for a clogged toilet vs IT for a bricked computer)