Yeah, pretty irresponsible for an article that says "all you need to know". You absolutely need to know the ins and outs of this if you have a significant number of options on a company with an increasing FMV. You own AMT on the paper gains between your strike price and the current FMV. However this only applies if you don't sell the shares. If you sell the shares before the end of the calendar year then the AMT calculation is nullified and you just pay taxes on your actual gains.
In a dotcom bubble scenario this can make the difference between owing millions of dollars of taxes despite having never seen a dime and owing your standard income tax on actual profits.