The author doesn't make a very spirited defense of his main point, because he distorts the neo-Brandeisian analysis of the effects of Amazon on business and employment into a question of whether the means Amazon used to achieve those effects are legal.
Modern Anti-trust is looking to see whether new standards should be applied to anti-competitive behavior, based on how the most powerful companies are affecting society. They're not trying to litigate whether our current megacorporations broke any rules to get where they are.
But even conceding that point, let's return to the introductory paragraph, What does it mean for a company to be Too Big? There are obvious answers, like how a company that is "too big to fail" holds the government and citizens as collateral when it gambles.
But what about something that applies to the tech monopolies more directly? Too Big to Manage. It's an absentee landlord type situation. Facebook allowing people to sell oxycontin and meddle with the US election comes to mind, but what about:
1) Good faith usage of Amazon can get you put on restricted traveler lists. https://lifehacker.com/your-amazon-order-might-lock-you-out-...
2) Amazon facilitates the sale of counterfeit goods, including pet food. https://news.ycombinator.com/item?id=16448001
3) It seems to be facilitating money laundering. http://fortune.com/2018/02/22/money-laundering-books-amazon/
4) And we've all seen the rest of the articles, about illegal drugs on amazon, about fake review scams, and more
Those are the points the author should address to counter anti-trust's uneasiness about amazon