"Currently pursuing a BS, MS or PhD in computer science or a related technical field." is verbatim from the intern job listing (http://www.google.com/support/jobs/bin/answer.py?answer=1262...), and I suppose it is there because the target audience for Google Engineering internships is students who are aiming to work some place like Google Engineering after graduating - not exactly the same category as "technically qualified students". So if you'd consider working at some place Google Engineering post graduation, then you should definitely apply.
For the record, I would consider economics to be a related technical field
(cf. John von Neumann, cf. "Evolution of Cooperative Problem-Solving in an Artificial Economy" - http://www.whatisthought.com/hayek32000.pdf)...
The clearest description of what CS researchers talk about when they talk about "intelligence" (see http://www.vetta.org/definitions-of-intelligence/) is probably a production function from economics.
Related only to this comment... I happen to be an Economics major as well. I'm graduating soon and am getting nervous about having to search for jobs/internships in this field because it seems most employers are looking for CS degrees. I have taken courses on Java and web programming in the CS department as electives, but most of what I know I've learned on my own. I don't really know much about theory.
Should I just be working on building my portfolio? I feel like the more I concentrate on my projects, the more my GPA suffers. I'm caught in a dilemma where I'm split between school and career aspirations, and that doesn't seem normal to me... or is it?
If I could do college over again, I would major in CS, but it's too late to change my major now. I had a horrible CS teacher in high school that initially scared me away from the subject.
I was originally an economics major, but I've managed to switch out into a major in math and a minor in CS (the study of AI was just too seductive). One area of CS theory that is pretty straightforward to pick up for an economist is algorithmic game theory: (http://www.amazon.com/Algorithmic-Game-Theory-Noam-Nisan/dp/...). There are also some strong connections to reinforcement learning and multi-agent systems (indeed much new research in computational economics is focused on multi-agent systems).
"The only hard and fast requirements for consideration are a strong programming background (any language(s)) and some experience in AI and/or machine learning."