"Paul's Case" is (mostly) sympathetic to Paul and (mostly) told from his point of view. He's got to be the protagonist, because there's really no one else to relate to.
At the same time, Cather doesn't give us much to work with. Even from the beginning, we get the sense that we're not really supposed to like Paul all that much. He's "hysterical," "conscious," and glassy-eyed (1.2), so not really doing much with the first impressions. It doesn't get much better, as Cather clues us into Paul's lying ways. Still, if we don't want to be friends with him, we certainly don't want him to end up in front of a train, and it's his downward spiral that we follow.
Sidenote—this whole thing of having a protagonist who's really hard to root for? You can thank the Modernists for that.