Their processing splits out individual sounds from longer clips, so the purpose is to browse those clips, not the full songs/recordings. Works quite well when you're hunting for things to use as samples in music production.
But regardless of that, once you've selected a clip, you can click "Play in context" to playback the sound together with what's before and after. And for the full song/recording, you can press "View on loc.gov" to play the entire thing.