The basic idea is that it is possible to build a market beating index using a method other than market cap weighting.
Of course this is absolutely true. We know that there are always going to be some portfolios that beat a passive index. The key questions are 1) will they do this over the long run, and 2) what additional risks are they taking on?
For example, in the article it is noted that the equal weighted index beats the cap weighted index. This is no surprise. The equal weighted index will have far more weight in small stocks. Small stocks tend to be riskier than large stocks, so a portfolio of more small stocks should be expected to outperform a market cap weighted index.
Also as pointed out in the article, the fundamentals weighted index is really a value stock index. While I am sure that this index is doing well right now, I'd bet that it would have done terribly in the 1990s when growth stocks were in the limelight.
At the end of the day though, you have to ask yourself: "if cap weighted indexes are so bad, why is it that they beat active managers at least 50% of the time?" These alternative index methods are just active portfolio management in disguise.