OK, that's a very confusing question but I think I've figured it out (uncertainty about "genes" vs "genetic material" notwithstanding).
I am almost certain that this calculation has not been made, for these reasons: as you say we don't have nearly enough information to make the calculations, even a partial calculations would be an enormous amount of work, which raises the question of what the purpose of this work would be, and I don't really see a use biologists might have for this number.
The reason it is an enormous amount of work is that most comparative genomic studies are done between a few species; to put all that information together you'd have to trawl through all those different studies. This is more feasible now with huge genomic databases, but it leads to the big issue: you can't just add all the genes in the different organisms, because most of those genes are shared between them. The closest thing I've found to a calculation of your "A" number is this paper:
If that were the total number of distinct genes in the biosphere then you could approximate the percentage you're looking for by dividing the total number of genes humans have by the total number of genes in the biosphere. Or you could get a better approximation by substracting from the total number of human genes the number of genes humans don't share with chimpanzees; I doubt it would change the number much though.
However that paper has an estimation of the total amount of DNA in the biosphere, a completely different issue from the number of genes, which is itself completely different from the number of distinct genes, which would itself rely on completely arbitrary distinctions because almost all genes vary between species, but if we count those small variations as "different genes" then obviously none of them are shared with humans at all, but there isn't a sharp line between "genes with different sequences that code for the same protein", "genes with different sequences that code for basically the same protein", and "genes with different sequences that code for similar but different proteins". The question is a bit easier with genetic material, but it's still clear that cross-comparing ALL genomes we have to list ALL of the distinct sequences is a computationally monumental task. And we're already using those computers for more immediately useful genomics analyses.
As for the issue of biologists having no use for the number, I simply don't see how knowing that number can increase our understanding about life, animals or humans compared to things we already know or are investigating, such as what genes humans have, what genes exist out there in the world, what relationship any specific human gene has to the genes of other relevant animals, etc.
I would like to know more about why you're interested in this number. You must certainly have a question in mind that having this number would help answer, and if we know that question it might be that there are other numbers, that have actually been calculated, that could inform it.
EDIT: Having said that it occurred to me you could still find things like the total number of distinct genes that have been identified by biologists in all living things, since that's more about counting the entries in various gene databases (this could also make a gene-based calculation actually easier than a sequence-based one). This would give at least bounds on the number you're looking for. In that spirit I found this paper about the total number of distinct genes in human gut bacteria:
Which appears to be 9,000,000, which would put an upper bound for the percentage human genes make up out of the total number of genes at 0.00025 or so. (you said nonhuman ANIMALS though, I don't know how strict you were about that factor)
REDIT - The number might be very different in animals actually, given these two papers :
Looking at the sequenced genome of a sponge and a coral respectively. The latter in particular has a convenient phylogenetic tree that illustrates how the sponge is the furthest branch away from us (i.e. our common ancestor with that sponge is pretty close to the common ancestor of all animals) and the corals branch off soon later. The former was estimated to have 30000 genes, of which 20000 were homologous to genes in other animals. The latter they found 25000 genes, of which 93% matched the genes of other metazoans. So we have something like 10000 genes that sponges don't share with us; 2000 genes that corals don't share with us; the numbers get smaller as we get groups that are closer to us, and presumably most of the genes, say, sponges have that are different from us are common between sponges, so you could get a ratio of genes in humans/genes in all animals that's as high as one half.