Not really. The fact is the human genome was much, much smaller than we realized, and about 30% of it is shared by most life forms. You’re not that much different than a banana.
What is important is not the genome (which is the software needed for building proteins), but the hardware that is needed to control it, and that hardware is embedded inside the cell. Equally important are the non-coding areas in the chromosome that many people don’t end up counting since they don’t encode proteins.
Sometimes this is referred to as Junk DNA. Junk DNA makes up the vast majority of our DNA. For example, we contain in our DNA almost the entire sequence of DNA to synthesize Vitamin C. However, the last step for building Vitamin C is damaged, and thus, unlike most mammals, we need to eat foods that contain vitamin C. Thus, the entire vitamin C synthesizing sequence is junk DNA.
However, some of that so-called junk contains instructions on how to read and build the encoding parts of our DNA. Some of the directions contain start and stop sequencing directions, so we’re not synthesizing proteins unless we need them.
So, the genome itself is quite surprisingly small (I think there’s 20,000 genes). But, the non-encoding DNA is much bigger (about 10x to 20x as big by some estimate). Much of that non-encoding DNA is junk, but some of that apparently contains important assembly instructions.
And, then there’s the structure of the cell itself which is needed to read the genome and actually do the building.
Think of it this way: The genome is like the user interface part of the OS that we see. It’s the Windows in Windows. The non-encoding DNA is the underlying part of the OS that builds the structures for the user interface to run. The cell itself is the hardware and built in ROM that’s needed to actually run Windows. Otherwise, that Windows CD ROM is just an expensive coaster.