Sounds more like a really nice overdriven mixing console to me, but a "Dumble" tone could really be anything, really. The somewhat splatty low-end in the recording isn't really typical of what people generally think of when they say "Dumble tone", but that doesn't mean that somebody couldn't dial one in to sound like that. Cool sound, though.
I don't know about Dumble, but that song is pretty cool and the guitar track is badass. I agree with the others, the distortion sounds like it came later. Direct and hot or at least post-amp. There's a million ways they could have achieved that distortion but it doesn't sound like a guitar amp to me.
The playing and tone reminds me a bit of Daniel Lanois.