What's the name of this effect?

Off hand, I'd probably call that effect "turning off most of the drum kit mics". It could be some type of filter, I suppose; but to my ear, it sounded like they turned off or down the kit mics, and just left a room mic or something to pick everything up with the "far away" sound.
 
That is indeed a resonant low-pass filter, with the cutoff frequency set to somewhere around 1.5KHz I reckon.
 
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