Roughly speaking, most of those genes seem to follow the tree pretty well. In general you can predict the gene presence or absense in some particular species by looking at it’s most close relative.
You are showing the opposite of what you are claiming. In all likelihood, the more genes we included to use for generating a phylogeny using presence/absence, the more likely it is we’d end up with the canonical phylogeny. Even in the tiny data set of 13 genes used in your figure, there’s obvious nesting hierarchical structure in the presence/absence of genes.