If BTC is treated as property (as the IRS says), then no. You'll only owe capital gains tax on it at the point where you sell or exchange it. Your capital gain will be the amount you sold it for minus the amount you bought it for, minus any expenses incurred buying/selling it. (If you sell it for less than you bought it for, you'll have a capital loss.) It's essentially treated like shares of stock.
That's actually not what is being talked about in the article at all. I think anybody would understand that if you make money by selling off your crypto, you would owe taxes on it, that's not what the article is pointing out. The article is pointing out that you may owe taxes on the value of crypto your received at a certain time, or traded for another crypto at a certain valuation, even if you never sold the asset for fiat money at that valuation. Meaning you could owe hundreds of thousands in taxes on an asset that never made you any money at all. That really is worth pointing out to people.
It's not by any argument just saying "pay your taxes".
The article outlines an interesting situation specific to bubble valuations like the dot com boom or (possibly) crypto currency in which you can easily end up owing far more in taxes to the IRS than the current worth of your holdings.
That, to me, is worthy of discussion and a front page place on a tech news site.
to emodendroket's point, I recall reading an article that in the previous year (2016) that the IRS stated that very few people were claiming bitcoins in their taxes. I'm not versed on cryptocurrencies so I don't know how plausible it is that they know this, but it seems like something they're looking at now.
Basically, only 802 people told the IRS about their 2016 profits in CoinBase, one of the more popular exchanges. It's safe to assume that number was a tiny fraction of the actual US users.
I imagine it is like anything else: they don't know, but if they do an audit or another agency is investigating you for something else and they notice, then they start investigating it.
I do think it is fair to say that there are more than 802, apparently, people in the United States in 2016 that mined/bought/sold bitcoin so they definitely see there is a problem.