re "If you listen to a song, you will immediately be able to see what rhythm it is (4/4, 3/4 etc), what bpm, where the breaks are, how much swing is appropriate, where the accents are etc." - I'm not sure I agree with that, although the rest of that answer seems good to me.
If there is an existing drum track, that must give you a huge clue as to where to start. But having just given some rudimentary drum lessons, my student asked how I work out when to start the basic rhythm, so that the rhythm fits the song. This made me realise that what's intuitive to me isn't obvious to everyone ! And I remebered having to learn this for myself.
If you want to try such drumming, and it's not that clear to you, try this :
Tap along to the song, and count 1-2-3-4. Most people can naturally feel the rhythm of a tune and tap in time to it. Normally, people will tap on the bass and then snare strikes (just intuitively - eg if you listen to a crowd clapping along to music). You'll end up with 1-2-3-4 = bass-snare-bass-snare. Sometimes it doesn't quite work and you have to do this half speed for slower songs or double speed for faster songs like Ace of Spades.
On your drums, play a bass drum and a snare as above along with the song .. there's your basic beat.
Note that I'm assuming the rhythm of the song is "even" ie not 5/8 or something odd, where this method will fall apart. Most popular music is pretty evenly paced.
This is probably how a lot of people gain the ability to drum along to anything.
As of there - for the song you linked to, the bass drum riff is accentuated to be more funky, which is where the feel for the rhythme comes in - and to be honest the choice. You can try a few things decide what you think works best.
For fills etc : It looks to me like this fella is going a bit wild and putting in everything he can think of which probably relies on experience ('this fill fitted with this rhythm last time I did it on another song..'), "muscle memory" and a feel for what he wants to project.