Upmarket where the real volume is, it is very hard to convince medium-sized businesses to pay a premium processing rate just to get a slightly enhanced POS, which itself has huge switching costs. For example we now know that the Starbucks deal turned out to be a loss for Square, a discounted fee probably justified as a marketing expense to get mindshare. Starbucks didn't value Square's product enough to actually pay a premium rate.
This is why I think the article is essentially spot-on in calling it a commodity product. Square is often compared to Apple, but Apple successfully decommodifies products through actual fundamental innovation (phones, MP3 players, PCs). They make stuff people actually want to pay premiums for. Square did innovate a cheap card reader, but beyond that it's mostly been beautiful design and attractive but unprofitable terms for the individual and micro business market.
Square Cash for example is pretty simple but it must be a money loser, since they charge no fee it costs at least 21 cents to do a debit transaction. Would it be as compelling if they charged 50 cents to send money? Beautiful design and all, probably not.
The moral to the story is that IPO-aspiring companies need to make products people actually want to pay premiums for, not just cool executions of commodity offerings that don't move the needle much in terms of actual utility.