Definitely invokes certain things for me too
There are endless ways to route the bits that are responsible for this too, in order to make those fluctuating, cyclical, and seemingly random white noise styles too. It can also make some really nice low rumbles when clocked low and running through a nice low pass filter with some envelopes modulating it. Like digital/game taiko sounds or something. 
Basically, a shift register just holds X amount of bits in a row (8 in the case of mine). A clock (or VCO for example) is sent to it, which moves the bits over by one position each clock pulse. You can feed the last bit into the first, so it cycles the data through indefinitely.
You can either load it up with bits (perhaps using latches with buttons for example) which would send the data through in a repeating cycle. OR, you can do other things, like sample in bits through a compator. Like send REAL white noise into a comparator, and anything read as high goes into the shift register as a 1, and anything the comparator reads as low, goes in as a 0. This happens as they shift down based at the rate of the clock/VCO.
So you can actually set up things that sound a bit more tonal, or completely random.
Most Linear Feedback Shift Registers (like Turing Machine, Noisering, etc.) take specific bits from specific steps (taps) of the shift register, run them through a loop of XOR logic gates, then feed THAT back into the input. This configuration is basically a pseudo-random number generator, which basically makes semi-quantized white noise, like the noise on the HexDrums. I’m guessing the HexDrums is using 16-18 bits which results in a very white-ish noise. Same as the TR-909.
This is actually how computers and game consoles generate random numbers for things, and also how many PSGs, SID, and other early sound generators create noise effects, which is why it sounds like old consoles and computers.
C64, Atari 2600, NES, Master System, Coleco, Intellivision all do this sort of thing for some examples.
Also, the bits can get fed into a simple DAC (in my case, an R/2R 8 bit DAC) which outputs a voltage for each combination of bits in the register, and that’s where you can get pseudo-random voltages for sample and hold style patterns (though a bit more cyclical usually)
Anyway, I’ll paraphrase Scott from Harvestman/IME and say “I’m a big nerd for shift registers.” 
More examples: