One, making them artificially is intelligent design and manufacture.
No it isn't. More on that later.
Two, they're only a raw material for making proteins which in turn are raw materials used in living things.
Which is why its only a piece of the puzzle. And not even a very large piece. But not irrelevant.
You mean the researchers weren't trying to make amino acids? Of course they were. They may not have known the exact amino acid they'd get but they were shooting for something.
That doesn't amount to design. There was no design, no blue print, no connecting one thing to another to build something, not even a series of planned out chemical reactions. JBS Haldane and Alexander Oparin speculated that conditions on the early Earth were favorable to making complex organic compounds from simple inorganic precursors. Stanley Miller and Harold Urey tested this by mixing gases that could have been part of the early Earth's atmosphere, at least around a volcano, carbon dioxide*, nitrogen, hydrogen sulfide, and sulfur dioxide, and adding energy**. Even if amino acids had been a specific target (and I don't think they were, it was just an attempt to see if more complex organic chemicals would form), I wouldn't call that design.
Other later versions of the experiments have produced more than just ammino acids. Substances produced include sugars, nucleotide basis (building blocks of DNA and RNA), alcohols, aldehydes and organic acids.
*CO2 is "organic" in the sense of organic chemistry. It has carbon atoms; but its simple, and common both where life is present and where there is no evidence of life. Edit - Or maybe not - "For historical reasons discussed below, a few types of carbon-containing compounds, such as carbides, carbonates, simple oxides of carbon (such as CO and CO2), and cyanides are considered inorganic." en.wikipedia.org
** heat, and sparks to simulate lightning |