A simple explanation is that these kinds of messages are not necessarily complete sentences. It wouldn't be unusual to see a message like: "item shipped", "item available", "item out of stock". It's possible in this context to drop the copula or the auxiliary verbs in order to save space. This was especially relevant in the time when paper forms were used which had limited space for grammatical, idiomatic language. This form is still used now either as an artifact (as in, people think that shipping orders should be written with this kind of language), or as a design decision (whoever made that webpage thinks less text looks better).
The other possibility is that this represents a shift in English usage, whereby verbs that were commonly transitive and not reflexive are now often used intransitively.
I don't have evidence that this is a new trend, but anecdotally, I've noticed this kind of thing a lot recently.
Here are some examples:
"We applaud Softview and encourage you to take a look at this unique product when it ships in April." (InfoWorld, 1990)
"The Apple Watch will also support Apple Pay when it ships in April." (Forbes, 2015)
"You will not be billed until it ships in April, 2020." (a random tweet, 2020)
And similarly with other "transitive" verbs:
"The film released on DVD and VHS in 2001." (Wikipedia, ???)
"Since the film released, film participant Frank Romano has published his definitive history of the Linotype Company." (Linotype: The Film, 2020)
"One of the most anticipated nights of the season unveils on Friday night" (Lernerville Speedway, 2019)
"The Last Blockbuster unveils on Friday, Sept. 21 during a block party in Bend." (KNCI FM.com, 2018)
