The little exclamation mark thingy is Illustrator telling you that the colour you've picked is out of gamut for CMYK (it can't be accurately reproduced in CMYK).
If you're having this printed onto adhesive vinyl, chances are it'll be done on some big poster printer thingy. Now, many of these are high-end colour proofing devices that can produce colours with a wider gamut than CMYK allows, since they have additional inks (they often have a light cyan and a light magenta in addition to process cyan/magenta/yellow & black). You may be able to print that blue more accurately, but you would have to specify it in some sort of colour model that the printer's RIP can understand, which probably means specifying it as a Pantone spot colour. If you know anyone who works in design/print, they could probably match the blue for you, by holding the original label up to a Pantone swatch book, or you could just take the original label along to the printer and get them to match to it. You'd have to physically compare the original label, you can't go from a photo since the photo is probably not colour accurate, as you've already discovered.
To reproduce the silver you'd have to do one of a number of things:
- have it printed using a proper spot colour metallic ink (prohibitively expensive for a one off print).
- print it onto a metallic stock (or print it onto clear film and mount it over a metallic stock)
- get just the Atari logo produced as a metallic rubdown transfer - many printing companies that specialise in producing packaging mockups will be able to do this. They scratch off though, so you'd have to get it laminated or something.
- or just put up with it being white or grey.