I definitely agree that parallelism isn’t held back by fundamentally serial work. Even with LZ decompression, most algorithms entropy encode the LZ sequences, and these sequences can be decoded in parallel with the LZ decoder.
Even if you couldn't parallelize decompression (non-entropy encodings?) there's nothing stopping you from breaking data up into multiple streams and separately (de)compression those. For games, this might be decompressing different assets simultaneously.
FWIW, my aim was to give an illustrative example of what I meant by a chain of dependencies, and your garden-variety gunzip foo.gz has one. You can certainly come up with compression schemes or situations where not everything has to be serial.