Ah, very interesting! Icon alignment is a tough one, but generally-speaking, more consistency is better. So if you have a table of primarily text, you’d want to keep things left-aligned, or if it’s primarily numbers, align things to the right.
That said, with the example you’ve cited there, I see a pattern that is commonly applied to data tables on the web: in addition to (or instead of!) providing tabular data, the layout also allows a user to navigate to more context about that item. Most of the time, I think this should be avoided if at all possible — turning a table into a navigation element instead of a reference element changes the context of design decisions, and can sometimes lead to a tradeoff of affordances.
One solution is to provide a single button that can wrap up all those links and provide a “navigation” context.
These can even be styled more consistently with text to avoid spilling more ink (though, that’s when the affordances get mixed):
However, the pattern I go to most frequently is the checkbox one employed by email inboxes everywhere, to enable a user to take action on a single entry, a group, or the entirety of the table:
Hope this is helpful. Thanks for reading!