How do I make something sound "cloudy" as though my ears are plugged using Ableton Live?
Do you have your kick on a separate track? If so, there is this cool plugin that will trigger a midi note depending on the sound input. You could use that to trigger a synth, or your own sample as Robert Harvey says.

As for transforming this sound:

First thing you notice is that there is a delay in the left channel. This reduces the impact as the sound is not heard simultaeously in both ears.

Second, the lows are cut. I'm guessing under 100hz things are not really happening. It's probably boosted a bit at 120Hz. Youtube is also having an affect on this. You should test this yourself with a high quality copy of this song in an analyser. AL (8?) has a pretty good one.

Third is there are not many highs. If your kick is a real drum kick, you'll need to eq the sound of the drum skin.

Fourth is some kind of FX: Maybe bit reduction and possibly some chorus. There are many ways to acheive this. If you want something warmer, you could also use some distortion.

However, all of this should really be applied reverse. At least the delay in the left ear should be added last so that the chorus (used to smooth out the harshness of bit reduction) does not sound like a "CHORUS".

They are using a constant delay on the drum kit. It sounds like a right-left-right delay. No center. AL has some FX for this. There is ping pong delay and simple delay. I'm not sure which one allows for panning (I'm not in the studio). But you'd want to delay back and forth between right and left channels with just enough feedback to only have three repetitions. Also the falloff (rate the sound volume diminishes) should be rather low, so that you continue to hear each successive delay clearly, rather that it getting quieter.

The beginning of the track, they've mutted the drum track on and off. It sounds like the kick and snare are being hit at the same time. You can automate this with envelopes in AL. This gives the impression that there is no delay and that the kick is sort of a double hit or has some kind of a reverse reverb on it. 

If you want to make something sound like your ears are plugged, you'd need to cut out a lot of the mid-range and high-end, as that is what is blocked. Considerable low-end still gets though. Though, I don't think that is exactly the sound you want judging from your example.