A position followed by a company name

I'm not sure about this one, but...

If it was one company, it would probably read, "Kinsella's chief technology officer" indicating the the person is the chief technology officer OF Kinsella ('s indicating the possessive like 'of' would).

In the example you give, it would have to be Kinsella and AS&E's or something equally unwieldy, and so it was probably changed for simplicity sake, or could just be a typo (I see them in the New York Times all the time).

To include 'the' you would need an 'of' to indicate the possessive, by omitting the 'the' you should have an 's to indicate that the CTO belongs to the companies in question.

The example was misleading. Kinsella is a last name of a person. AS&E is the name of the company. So the question really is:
Which is correct:
"AS&E chief technology officer Joseph Callerame usher me into ..."
Or
"The AS&E chief technology officer Joseph Callerame usher me into ..."

The job title lost its initial article, not because it was preceded by the name of the company, but because it was followed by the name of the jobholder. This becomes clearer when you remember that "Senator" is likewise a job title:

The Senator walked into the room.
The CTO walked into the room.

Senator Foghorn Leghorn walked into the rom.
CTO Ferdy Longbottom walked into the room.

If you separate the job title from the jobholder's name by inserting a comma between them, the job title stops being part of the person's name and gets its initial article back:

The CTO, Ferdy Longbottom, walked into the room.