This list is just problematic...
The list itself has books I have never even heard of, much less read. I'm a pretty broad reader of fantasy these days and have my own library of thousands of books (one of the largest library collections of fantasy books in the area from what I can tell). That doesn't really qualify me, as it is more of a local thing, but many of these books were not even considered to be in my library. They were not considered to be important enough to be in the public libraries around here (so good luck at even borrowing it in the local library system, they'd have to go out and request it from outside the local network)...
This list shouldn't be taken seriously by anyone I think.
It isn't THAT hard to make a list of the 100 most influential fantasy books today and have most of the books as something most would recognize, or one that those in the hobby would recognize almost every book as being an important facet in the hobby.
Here's one that seems a LOT MORE relevant and actually knows more about what it's talking about.
Top 100 Fantasy Books
Still not that great or perfect by any shot, but more on spot than Time's I think. Still many problems, but at least the top looks like what I'd think a list of this sort would start looking like.