Usually you don't get a subscription and in this case it looks like access to a part of their website, rather than a print edition.

Music competitions are different. Do they generally issue a hard copy of the winning entries? Literary magazines often do. Not only that, but their websites generally get fewer clicks and are unlikely to be supported by advertising. Most lit mags make no money.

Not only that, but entry fees do help trim down the submissions to more manageable numbers. Technical skill in writing is not as obvious with writing, partly because people tend to think that because they can write (sentences, their name, etc.) that they can write (stories, poetry, etc.). With music, it becomes pretty clear pretty quickly whether or not one has chops. Also, an amateur piece of music tends to get feedback more quickly and across a wider audience than a piece of amateur writing. Thus, there are a lot of submissions.

Entry fees are rational from the viewpoints of people that have to deal with submissions, though it may not be so from the viewpoint of people submitting work.