It may be thought that our understanding of evolutionary science deals a fatal blow to the "argument from design". But even if natural selection can be shown to be the explanation for all the complex biological phenomena we find, this just presents more questions: for example, why is the periodic table structured in the way it is, allowing chemical reactions to occur in the way that they do which makes life possible?
However, Hume's critique of the "argument from design" is not based on alternative explanations for natural selection; it is an attempt to refute the logical basis of the argument. Hume doesn't set out to provide an alternative explanation to the divine designer, and he doesn't even seem to disagree with the idea that the universe has the appearance of being designed. Instead, he sets out to show that it is not reasonable to infer the existence of a designer based on our own empirical knowledge.
The points Hume makes might be reasonable enough, but overall the passage does not seem very satisfying: he does not refute the argument, just shows why it can be regarded as doubtful. In fact, the level of proof he appears to require is impossibly high. He says
The only experience we have to work with is that of the small fraction of the universe that we inhabit, and we the only reasoning ability we have to work with is the human mind, and so Hume is right to say we are constrained by those limitations. And perhaps those raw materials don't provide enough to be able to conceive of the ultimate explanations for the universe. But does this mean we should give up altogether?
I think that Hume has shown that the "argument from design" has flaws, and so may not be regarded as a "proof". However, the fact that it is not "proof" of God does not discredit it altogether.