Vertical, horizontal, or matrix?
It's all three! Because this is really two intersecting lists—names running down, and dates and events running across—with consistent properties for every item.
I'd say that it's closest to a matrix, because it's so rigidly structured.
You could lay it out like this:
Name | Season | Month | Day | Reason
Ordering
It's both ordered and unordered. The names appear random (though there could be an order we don't see). The reasons are ordered by date, so they are sequential.
Hierarchy
In the simplest terms, there are 2 levels of hierarchy: name and date of absence (+ reason).
If you wanted to make the list seem more organised and make the categories more obvious, you could rewrite the list like this, for instance:
-Name
---Season
------Month
---------Day & Reason
List items
This is tricky! It depends on how you want to use the list!
If you want to know how many days a worker was absent, then the list items are the days absent, not the reasons for the absence!
We notice the reasons, but when you think about it, the reason is just a property attached to the day.
However, if you wanted a list of reasons that workers give for being absent, then the list items are the reasons for absence. (But if that's all you wanted, then why do you need the names and dates!?)
➡️ This list is actually a very early example of what we now call a database: a collection of related items that you can query in different ways. 🤯
Level of detail
Each item is minimally detailed.
