Making the decision to work those two months for free is a toss up. Are you guaranteed the internship position?
I don't know how internships work in terms of taxes, benefits, labor laws and other legal stuff, so I'm not sure if the reason there is no pay because it's only 2 months, or if they just don't/can't pay at all. The no pay is a bit of a red flag though. If it's a successful company or new startup, they should have the money to pay you a livable wage for 2 months. I haven't heard of too many places that still do that nowadays.
What is the reputation for the company? Do they have talent or a good history? This can probably go one of three ways: first, you could waste 2 unpaid financially stressful months and learn absolutely nothing while making lens flares and dust motes and getting coffee. Second, you could learn a lot, but be given a huge work load and basically do a chunk of the company's vfx work for free. Third, it could be equal parts learning and workload, where you would learn some good skills, get a feel for the workflow of a studio, and get a few things into a game and your demo reel.
With no more information than what you gave us, you have to determine yourself if the cost will outweigh the benefit or not, or if you will benefit at all.
I'm sorry that isn't too much help, but some stuff to think about. There are as many internship horror stories about people's work getting stolen or doing a bunch of work for free with no pay off as there are success stories. We don't want you to fall into the former.