It doesn't really seem like the authors fully understand Git, and what problems it solves.
> [...] in Git each commit is related to a parent [...] But in Pijul there's no timeline and branches are just sets of patches.
To me, that makes Pijul much, much less capable as a version control system. In Git, knowing the commit ID means that you know the full source tree state with the certainty being equal to the risk of a commit ID hash collision.
With just individual, unrelated patches applied in sequence, you have no such guarantee, and no knowledge of the current state of the repository.
Of course, you could add a seperate state tracking system allowing ID's to point to an immutable and unique set of patches in a certain sequence, but doing so just means that you have now implemented features identical to Git, with just a different internal representation (i.e. irrelevant differences for the user).
> [...] And push those changes in whatever order we want
You can do the same in Git (see interactive rebase, cherry-picking, similar). It rewrites the commit IDs in order to maintain the previously mentioned property of representing the state of the repository, but that's an implementation detail.