It's all very Contemporary Classical, with some Jazz added for flavor. Maybe an investigation of Late 19th and Early 20th Century works would help provide context. It's a lot of controlled chaos going on there, especially on The Civil Surface (technically a posthumous release by the band).

From PA page on them:  " The music is very structured and composed, with classical pieces (BACH) and some light jazzy influences. The band explored a variety of time signatures and key relationships, sometimes explored classical ideals, and even composed their own symphony.."

I'm not sure if there's really a lot beneath the surface on something like Boilk; it just sounds like a short experimental piece. It may help to understand a bit about the Mellotron; which had two types of tape banks. One would have a single note per key, so if you wanted to hear strings playing an A, you'd just press the A key (you could transpose with a Pitch knob, so your A key now plays a G, for example - this is what causes all the pitch sliding in this particular track.) The other type would be a set of loops, so a key would trigger a short drum pattern, or a short melody. It sounds like the guitar is Boilk is based off of these loops, but only letting the first one or two notes play. This is why it sounds so choppy and repetitive; you're hearing the same few samples over and over again - sort of a precursor to what DJs and Hip-Hop artists would do.

Might be a bit easier to hear it rather than read about it: