Shares are not options, and any business magazine is aware of the difference. Exercising options is also not selling anything: it is a stock purchase for the strike price of the option.
Trust me when I say this, I know EXACTLY how stock options work. I have exercised a bunch of them. Not in the millions, obviously, but in the several tens of thousands.
Nobody, and I mean NOBODY, can exercise their stock options for the strike price. To buy out $20M worth of options usually involves a short term loan of $20M (by the company) to purchase the options which is repaid out of the sale of the shares. It's done all the tiime...
I went to work for a company and they gave me a bunch of options with a $50 option price. A year later, when they could be exercised, the stock was trading at $26. To their credit, the company renegotiated all of the options issued the year I was hired.
Start-ups do a lot with options but there is the risk that the entire venture goes down the drain. Established companies also try to motivate key employees with options. The company does well, the employees do well. A side issue is that the options can't be exercised before a certain date - helps with retention when the share price is higher than the option price.
There is no way a CEO buys stock in his own company out of his own pocket. Part of his compensation package will include a bunch of options. If the CEO drives the company upward, the options are part of his compensation and motivation.
I don't know exactly how the CEO of Intel is rewarded but I would bet that there is company stock grants or options involved somewhere. Nobody works for wages at that level.