I just took a quick listen on my laptop, so I could be wrong, but I don't think the snare is mono. In fact, it sounded almost excessively stereo. Some kinda slappy-room ambience in wide stereo bouncing around or something.
Anyway, yeah, you want that drum sound, just turn it up loud, add a slappy-room ambience in wide stereo.
The backing arrangement helps, in that there's not a heckuva lot of upper midrange information masking the drum sound. I also wonder if the perceived volumes of the midrange and top of the kick and hats (which are low, relative to the snare) don't force the snare to the front of the balance. If you imagined a real drummer playing that groove on a real kit, he'd be NAILING the snare, and just barely touching the kick and hihat.