This isn't credit card arbitrage. Let me describe one idea for how Credit Card Arbitrage could work.
You take out a bunch of credit cards, as he describes. Preferably ones with zero interest for the first year, or 6 months. You extract as much cash from them as you can. You put a chunk of that cash in the bank to make minimum payments from, and then you put that cash into an asset that will return more over the next year than the cards will charge.
[EDIT TO ADD: Want to clear up some confusion. In order to arbitrage interest rates, you have to have whatever you buy return more than what you have to pay for the money. There's one factor that people often forget when thinking about interest rates, and that is inflation. Dollars spent to pay off a loan are worth less than dollars you get at the beginning of the loan. This means, the asset you put your money into, needs to return not only enough to cover the interests & fees on the credit cards over the time period, but the monetary inflation rate over the time period. Thus, something that is an inflation hedge is beneficial. This is why I talk about gold below, and later I talk about CDs and even stocks.]
I'd suggest buying gold, or gold miners, or if you're super sophisticated, options on solid gold mining companies. (each of these has increasing leverage to the price of gold.) But it doesn't have to be gold, it just has to be something that is a "no brainer" way to earn a positive return above the rate of the credit card interest.
This may be difficult, and in fact, it should be difficult, because if it were easy the credit card companies would do it instead of loaning the money to you.
Potentially, you could take the money from the credit card company and put it into a CD at the very same bank. This works only if you really have "no interest for one year". Buy a 9 month CD (or better yet a 10 month CD), and then when it matures, pay off the credit card, and you get the interest from the CD for free.
The thing that makes such arbitrage opportunities so valuable is that, because the asset you're buying returns more than the cost of your money, you can scale it up pretty much infinitely.
But this is where things get problematic if you don't cover your downside. When the Bank of Japan was lending money at nearly zero interest, many banks borrowed in japan, converted the money to other currencies, and then bought treasuries of other countries. This is called the carry trade.
In fact, I wish I could start up a bank right now. I'd love to borrow money from the Federal Reserve, which is loaning it out at almost nothing, and buy the best bonds (along with some protective put options) I could find on the market.
A company wants to borrow for capital expansion, it will pay a reasonable interest rate-- say %6. The Federal Reserve is loaning at something like %1. %5 profit, at the only risk of the bond (so protect it with a CDO.) It must be great to be a bank.
If you have a startup you need to fund, and you can get a CD the interest rates right now are about 1.15%. So, I think this doesn't work for arbitrage, because while you may have "zero percent interest" there are going to be some fees that will overwhelm that meager interest rate.
But, if you could get a CD that paid out %6, and could borrow at %1 (on the "zero interest" plans) then you'd only need $400,000 in credit card debt in order to raise $20,000 for your startup!
Realistically, credit card arbitrage doesn't really work too well. If you get something with a higher rate of return, and you use borrowed money to buy it, then that's really investing on margin and not really something you could call "arbitrage". I'm sure it works for some people doing startups.... but isn't really reproducible on a wide scale.
BY the way, if you want access to some of that federal reserve money at cheap rates, at least some brokers are passing it along to their margin customers. Then you can start looking for a solid high yielding company, borrow %50, effectively doubling your yield... don't forget to buy some put options to cover your long position in case it crashes.