I would take Warren more seriously if she started out by talking about ATT/VZN/Comcast. The "big tech" companies have the potential to harm consumers, but telcos have been harming consumers for decades.
Warren's argument here is a straightforward free market one: free markets only work when there's a free flow of information. If Amazon both runs the market and participates in it, it's an inherently unfair playing field. Her argument is not that we should break up companies that we don't like or even those that hurt consumers; her argument is we should break up companies whose intact existence threatens the fundamental nature of free markets.
All that said, as it happens, she opposed Comcast's attempt to buy Fox https://thehill.com/policy/technology/396559-senate-dems-urg... and the T-Mobile / Sprint merger https://thehill.com/policy/technology/429618-dem-senators-ur... — opposing both on the grounds that they're anticompetitive.
to substantiate this point: https://news.ycombinator.com/item?id=15890551
Should grocery stores and Wal-Mart not be able to sell store brands?
Should Xbox Live and Playstation Network not be able to sell first and third party titles?
I think the argument is stronger against hardware manufacturers locking down their devices to only first party app stores, than against regular shopping. If I buy a phone from Apple I can only run the apps they approve, and when they stop supporting the OS, the phone doesnt unlock and allow me to install my own OS. Apple can obsolete hardware by strongarming a lack of updates to crucial banking and communication apps.
If she actually believed this, it would be a fundamental misunderstanding of FCC. FCC helps monopolies and hurts consumers because that is its purpose, since 1934. Neither Democrats nor Republics have ever done anything to change this. Net neutrality is a fine network policy, but it wouldn't need to be mandated by regulation if actual competition existed in this market. FCC throughout its history has acted mostly to prevent such competition.