That's what the Estate Tax is for. There are ways to circumvent that via things like charitable foundations, however that's a very different debate.
The author is confusing income from dividends (either of the stock or bond variety) and interest income with income simply for existing. He chooses to use Alaska, an oil rich and low population state, as a model for the rest of the country. He states that the government would somehow build up a "big wealth fund" that would deliver "returns" without specifying where those returns would come from or the amount of those returns. A fund of the size required can't easily generate large returns since that amount of money is enough to distort markets.
Simple back of the napkin math is that based on the 2013 census, we have 242,470,820 adults living in the US. If we pay each of them $12,000 per year, that's
$2,909,649,840,000 in additional mandatory spending every single year. That's more than Medicare and Social security combined, and that has no cost of living adjustments built in. The basic math shows that this idea is simply unrealistic as far as I can tell.