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also were the boxes otherwise identical? were the unbranded boxes obviously empty while the branded boxes always had shoes in them?

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From the article it looks like these were all regular shoe deliveries and they chose either to add the branded tape or leave it off. So from a weight/contents perspective there shouldn't have been much difference.

The article does not say that. It says that every person was sent two packages.

They are shoes. It's pretty easy to assume how they split a pair into to equally weight & size packages for the test.

Sure you could assume that, they didn't say so though.

As an experimental design that would be pretty good, but as a product experience I would not be very happy to unbox one shoe, then wait days for the other one to arrive or find out it was lost in the mail.

One shoe in each.

Do they actually say that anywhere? It's a pretty logical way of doing it but it's still an assumption about a pretty important facet of the experiment.

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