You might also try resampling it to something like 32,000 Hz, 22,050 Hz, or even 16,000 Hz. Basically this will be removing some of the high frequencies the way a low pass filter would, but in a subtly digital "lo fi" way. I can't really tell if that's what they did here, but it might've been part of it. Some of the original sampling equipment only went up to 32,000 or 22,050, so sometimes that's part of the old school hip hop aesthetic.
To do that, either use a wave editor like Audacity/Wavosaur, or... wait, y'know what, just use
TB TimeMachine--there's a free version included in the trial plugin pack (just follow the "download evaluation" link or whatever). I might also suggest playing with JB Ferox, but I don't think it's available anywhere anymore. (It's been replaced by the no-longer-free TB Ferox.)