A long time ago, we had turntables with 16 RPM, then Ibanez came out with a small cassette player that had a half speed switch called the Rock and Play. Those gave way to the Tascam CD-GT1 guitar trainer, and after a few years it became a MP3 version.
Nowadays, we can just use the gear icon on youtube, and slow down any song to quarter speed if necessary...at the same pitch even!
I tell ya, younguns got it so easy, LOL!
As for that song section, it sounds as if the bass guitar hits are exactly on the bass drum hits, as he keeps 16th ticks on the hi-hats. I would slow it way down, and play along till I got it, then move up to the next speed, and get it there, and so on...
Counting it out definitely works, but IMHO, it's more important to feel it out, otherwise it seems more like math, LOL!