It looks like there's some layering going on with the snare and of course some reverb. It doesn't sound like a regular rock or acoustic snare IMO (I could be wrong) but more like a processed hip hop one. Try grabbing some free hip hop drum samples around the internet and adding some distortion from something like Camelcrusher (free plugin and one of my favorite) and some reverb that simulates a drum room recording.
orchestral bass drum (for the kick sound) and an orchestral snare over the top - both recorded in very live rooms or having a very pronounced reverb added to them
the orchestral snare is playing ruffs (3 or 4 notes per stroke) whilst the orchestral bass drum is a single hit each time