Iron law "might be"?
I don't think I'd ever invest in Box, but I see Square much differently. I think the author arbitrarily pooled them into the same category, and then stumbled over his own argument throughout the article.
Square is in a market where once you have a customer, you have the customer. There's not really a reason to switch your payment processor unless your experience with them is particularly terrible, or processing fees dramatically change in the market (not likely at all). They're building a solid revenue stream, and their numbers back it up. Unlike Box, they're hovering around profitability, not hemorrhaging money. They certainly have some stiff competition, mainly Paypal, entering the market, but Square is offering a more comprehensive experience for business owners, not to mention a much smoother product. I can't tell you how many times I've seen a whole line of customers stumble over how to complete a transaction on Paypal's offering.