ISTjs don't like to be in the spotlight, they don't like to present and show themselves (and thats what body-building in the style Arnie did it is), ISTjs don't have that much self confidence, and there determination comes more from stubborness than from will power.
and yet Julia Roberts is an ISTj... istj celebs.

Look at some of the other ISTj's on that list. That verifies that it is possible for a celebrity to have that type.

It is just a possibility.

Extroversion would explain some of this as well. This site types him as an ESTJ.

INTj does not seem likely, since you are going by stereotypes here, I can too - INTjs are not typically considered athletes. He could be INTj with a low N score, which would make him nearly ISTj. However, ask yourself if INTjs like the spotlight.
My new verdict is ESTj. Athletes are typically ST. J is because Arnold is demaning of himself, and has high standards.